I've run 32c tires like forever on mod e rims and I'm pretty sure I've run fatter tires as well. There is an easy way to find out. Mount the tire on the rim and pump it up 10-20 psi over the recommend max. If the tire doesn't blow off the rim, you're good to go.

Agree with the other posters that the frame may give you a problem with a 35c (and if the frame doesn't, the front derailleur may give you some rub depending on how long the chain stays are) and that 32c is plenty wide enough.

I just knocked out my 20 mile training ride on a bike with 32c tires. I hadn't ridden the bike for a while and I'd forgotten how comfy they are.