Well, it might fire but it will certainly swell and possibly split the smaller diameter 32 S&W Long case. It shouldn't harm the gun though as it is a much lower pressure round than the tapered 32-20 (which is noticeably larger at the case head).

Some people have been shooting 32 Longs in the Russian Nagant revolver which use a case dimensionally similar to the 32-20 and split or swollen cases are common. Some recommend putting a wrap of tape around the 32 Long case to tighten up the fit.

I don't recommend shooting the wrong round out of a gun myself but it's a common topic on the Nagant section at Gunboards. At least with this substitution there's little chance of blowing the gun up.