Should I install baseboards before or after skimcoating?
I would put on the baseboards, but only tack them in place so they can easily be removed when the drywall guy is done.

The reason he is probably asking you to install them, is so he can make sure you are happy with the finish before he leaves so he doesn't have to come back.  

It's probably a good idea anyway, because it would be a shame to get all the painting done only to realize the baseboards don't fit right.  Then you would have to start all over again.