Do vector drawings colored in with Illustrator's Live Paint work as expected for use in a responsive website?
Yes, but you probably need to Expand the objects in order for proper compatibility.
You can use Live Paint to color everything in.
Now go to Object → Live Paint → Expand in order to expand the paths into regular paths that are independent of the Live Ppaint group.
(You can also use Object → Expand and only select Objects - it seems to produce the same results)
You can test it like this.
- Export your work as an SVG.
- Upload it to SVGshare(dot)com
If you can see it as intended, then it will work on any website, whether responsive or not. Check the svgshare link in other browsers, and on your phone/tablet, etc.
Here's a live paint object exported as an SVG, and it works as expected.
Note: I have no affiliation with svgshare.