Would a Portland Design Works 700 x 37 fender fit a 700 x 32c tyre?
It's never going to work great, but whether it works at all depends on how much vertical clearance you have to work with. When you push the tire size, what happens is the fender can't wrap around the tire properly, and instead the tire wants to rub against the "gutter" or side of the fender. If you can simply gap the fender further away, you might be able to get by, but many bikes won't give you the ability to do so sufficiently.

Having this little overhang tends to result in an installation that needs readjustment all the time and wants to rub. 

Also the actual inflated width of the tire is important here, especially since rim width can have a major impact.