Is it possible to disable onclick without altering its function?

You can do it in css.

<button onclick="alert('clicked')">Can click</button>
<button onclick="alert('clicked')" style="pointer-events: none;">Cannot click</button>

Pro: it works on all HTML elements

Con: it doesn't prevent keyboard action

Use the disabled attribute to disable a button.

<button onclick="alert('clicked')">Enabled</button>
<button onclick="alert('clicked')" disabled>Disabled</button>

The advantage of this method (over the "pointer events" suggested in an alternative answer) is that it will not only stop you using the button as a mouse user, but will also stop assistive technologies and anyone using the keyboard.

In JavaScript, you can disable or enable the attribute with:

el.disabled = true;   // Disable.
el.disabled = false;  // Enable.

Or with jQuery you can do:

$('button').prop('disabled', true);   // Disable.
$('button').prop('disabled', false);  // Enable.

You can do it like this

<button onclick="false && alert('clicked')">Try Click (Disabled)</button> 

<button onclick="true && alert('clicked')">Try Click (Enabled)</button>

It will work for both click event and keypress event.

<button onclick="false && alert('clicked')">Try Click (Disabled)</button>

<button onclick="true && alert('clicked')">Try Click (Enabled)</button>