Is it possible to have a block cursor in sublime text 3?

You can try out the package that @user2365566 mentioned. I personally didn't like the way that cursor looked.

Here is an alternative, just add following into your Preferences.sublime-settings:

{
    "caret_extra_width": 5,
    "caret_style": "solid",
    "wide_caret": true
}

You can change the caret_extra_width number to whatever you like, based on how wide you want the cursor to be.

This is now possible as of Build 3190 (from 19 February 2019). You can enable this with

"block_caret": true

in your user settings. Your theme may not have a style for this, so if the default color of the caret isn't to your liking, it can be changed in your theme by adding

<key>blockCaret</key>
<string>#FFCC00</string>

into your theme's settings section. It will look something like this: