Generally they will melt the foam from what I've experienced. Lacquer/solvent based vs. acrylic.
The acrylics I've used don't seem to adhere to foam very well. Could be the brands I was using.
What I have done is I've bonded card stock or thick tissue paper to the foam using thinned white glue, thinned carpenters yellow glue or very thinned gorilla glue on some of my rc foam planes when repairing after some unwanted directional changes :|
Seal it up after or give it another coat of thinned glue to seal and thoroughly dry for a few days, very light sand with fine grit paper and then it will take a rattle can of any type without issue.
The same method would probably apply to what you are doing but best to test on some scraps to be sure :)
-Colin.