use transition on ::-webkit-scrollbar?

Here's another idea based on replies here. You can use color instead of background-color and then box-shadow to colorize the thumb. You can use -webkit-text-fill-color to color back the text:

https://codepen.io/waterplea/pen/dVMopv

*::-webkit-scrollbar-thumb {        
  box-shadow: inset 0 0 0 10px;
}

div {
  overflow: auto;
  -webkit-text-fill-color: black;
  color: rgba(0, 0, 0, 0);
  transition: color .3s ease;
}

div:hover {
  color: rgba(0, 0, 0, 0.3);
}

It is fairly easy to achieve using Mari M's background-color: inherit; technique in addition with -webkit-background-clip: text;.

Live demo; https://jsfiddle.net/s10f04du/

@media screen and (-webkit-min-device-pixel-ratio:0) { 
  .container {
    overflow-y: scroll;
    overflow-x: hidden;
    background-color: rgba(0,0,0,0);
    -webkit-background-clip: text;
    transition: background-color .8s;
  }
  .container:hover {
    background-color: rgba(0,0,0,0.18);  
  }
  .container::-webkit-scrollbar-thumb {
    background-color: inherit;
  }
}

Adapted from @brillout's answer, if we transition the border-color instead of background-color, we can avoid using background-clip: text, which leaves some fragments behind if you have any nested text.

Full explanation:

1. Place your content inside some wrapper div and then add a transition to border-color on your wrapper to change the color on hover.
2. Add an inset border to your scrollbar, and set the width large enough fill the entire element.
3. Set border-color: inherit on your scrollbar.

Now when we hover over the wrapper, the border color will transition. The wrapper doesn't have a border, so we don't see anything happen. However, the scrollbar is inheriting that color, so the scrollbar color changes.

Here is the most important code. A full example is available in this fiddle and the snippet below.

#scroller {
  /* fill parent */
  display: block;
  width: 100%;
  height: 100%;

  /* set to some transparent color */
  border-color: rgba(0, 0, 0, 0.0);
  /* here we make the color transition */
  transition: border-color 0.75s linear;
  /* make this element do the scrolling */
  overflow: auto;
}

#scroller:hover {
  /* the color we want the scrollbar on hover */
  border-color: rgba(0, 0, 0, 0.1);
}

#scroller::-webkit-scrollbar,
#scroller::-webkit-scrollbar-thumb,
#scroller::-webkit-scrollbar-corner {
  /* add border to act as background-color */
  border-right-style: inset;
  /* sum viewport dimensions to guarantee border will fill scrollbar */
  border-right-width: calc(100vw + 100vh);
  /* inherit border-color to inherit transitions */
  border-color: inherit;
}

<div id="scroller">...</div>

body {
  background: whitesmoke;
}

#wrapper {
  width: 150px;
  height: 150px;
  margin: 2em auto;
  box-shadow: 0 0 15px 5px #ccc;
}

#scroller {
  /* fill parent */
  display: block;
  width: 100%;
  height: 100%;
}

#content {
  display: block;
  width: 300px;
  height: auto;
  padding: 5px;
}

#scroller {
  /* The background-color of the scrollbar cannot be transitioned.
     To work around this, we set and transition the property
     of the wrapper and just set the scrollbar to inherit its
     value. Now, when the the wrapper transitions that property,
     so does the scrollbar. However, if we set a background-color,
     this color shows up in the wrapper as well as the scrollbar.
     Solution: we transition the border-color and add a border-right
     to the scrollbar that is as large as the viewport. */
  border-color: rgba(0, 0, 0, 0.0);
  transition: border-color 0.75s linear;
  /* make this element do the scrolling */
  overflow: auto;
}

#scroller:hover {
  border-color: rgba(0, 0, 0, 0.1);
  transition: border-color 0.125s linear;
}

#scroller::-webkit-scrollbar,
#scroller::-webkit-scrollbar-thumb,
#scroller::-webkit-scrollbar-corner {
  /* add border to act as background-color */
  border-right-style: inset;
  /* sum viewport dimensions to guarantee border will fill scrollbar */
  border-right-width: calc(100vw + 100vh);
  /* inherit border-color to inherit transitions */
  border-color: inherit;
}

#scroller::-webkit-scrollbar {
  width: 0.5rem;
  height: 0.5rem;
}

#scroller::-webkit-scrollbar-thumb {
  border-color: rgba(0, 0, 0, 0.1);
  /* uncomment this to hide the thumb when not hovered */
  /* border-color: inherit; */
}

#scroller::-webkit-scrollbar-thumb:hover {
  border-color: rgba(0, 0, 0, 0.15);
}

#scroller::-webkit-scrollbar-thumb:active {
  border-color: rgba(0, 0, 0, 0.2);
}

<div id="wrapper">
  <div id="scroller">
    <div id="content">
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  Maecenas felis quam, ultrices ac ornare nec, blandit at leo. Integer dapibus bibendum lectus. Donec pretium vehicula velit. Etiam eu cursus ligula. Nam rhoncus diam lacus, id tincidunt dui consequat id. Ut eget auctor massa, quis laoreet risus. Nunc blandit sapien non massa bibendum, ac auctor quam pellentesque. Quisque ultricies, est vitae pharetra hendrerit, elit enim interdum odio, eu malesuada nibh nulla a nisi. Ut quam tortor, feugiat sit amet malesuada eu, viverra in neque. Nullam lacinia justo sit amet porta interdum. Etiam enim orci, rutrum sit amet neque non, finibus elementum magna. Sed ac felis quis nunc fermentum suscipit.

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    </div>
  </div>
</div>

Short answer: No, it's not possible to use transition on a ::-webkit-scrollbar

Long answer: There are means to achieve a similar effect entirely in CSS.

Explanation:

1. We need to create an outer container that will scroll. Then we want to create an inner container.
2. The outer container will have a background-color property. This property will match the color we want to transition on for the scrollbar.
3. The inner container will match the height of the outer container and will have a background-color that masks the outer container.
4. The scrollbar's background-color will inherit the outer container's.
5. The transition property will be applied to the background-color of the outer container.

A major disadvantage here is that you have to do some masking. This can be a bit of a hassle if your background isn't a solid color, since the inner container will most likely need to match. If that's not a worry, this will work for you. Here's the code to put it all together for a page with a horizontally scrolling component.

HTML

<div id="container-outer">
    <div id="container-inner">
        <!-- Content goes here -->
    </div>
</div>

CSS

    /* Scrollbar */
    ::-webkit-scrollbar {
        border: 0;
        height: 10px;
    }
    ::-webkit-scrollbar-track {
        background: rgba(0,0,0,0);
    }
    ::-webkit-scrollbar-thumb {
        background-color: inherit; /* Inherits from outer container */
        border-radius: 20px;
    }

    /* Container */
    #container-outer {
        overflow-y: hidden;
        overflow-x: scroll; /* Horizontal-only scrolling */
        height: 400px;
        background-color: white; /* Initial color of the scrollbar */
        transition: background-color 200ms;
    }
    #container-outer:hover {
        background-color: red; /* Hover state color of the scrollbar */
    }
    #container-inner {
        background-color: white; /* Masks outer container */
        font-size: 0;
        height: inherit; /* Inherits from outer container */
        width: 10000px; /* Set to see the scrolling effect */
    }

Notes:

• It should be obvious, but this is a Webkit solution. The question was specifically about Webkit and not anything else, so this answer is only in regards to Webkit.
• Your outer container will probably need a max-width that will match whatever your inner container's width is, otherwise you may see some oddity on extremely large displays. This is an edge case for when the browser width is larger than the horizontally scrolling content width. This is assuming you are using a horizontal scroll, as the example code does.
• Hovering styles don't work as intended on mobile in most circumstances. This is an issue given how there is a huge market penetration of Webkit mobile browsers. Take that into consideration before using this solution.