Unless you're dealing with several dozen cars arriving at once, it should be reasonably distinct, and even if for some freak reason there is more cars than colors, it'll still help sorting through prospective cars more quickly.
You could also do this automatically, but offering the user control over it may help them feel in charge and/or remember the color they picked better than just assigning one.
That's my thoughts on it.
If you don't care about the color the light is, you'd simply confirm without changing anything.
Another nice tweak would be coloring the app based on your chosen color whilst you are waiting for the ride, making the connection obvious. That should be a fairly simple matter of shifting hues.
Hrm, thinking about it, it'd probably also be neat if it tracked what colours users who do choose pick, and then use that information to deduce their favorites. If any of those are available, it should pick them automatically. Even if I went out of my way to pick orange every time, it'd be nice if the app remembered that and picked orange for me, thus eliminating a step.
It may be worth displaying available colors as smaller squares next to the button like this:
┃ primary ┣━╋━╋━┫