The 32 H&R is long enough that it should get the neck up at or close to the neck area of the 32-20 chamber so it would be supported at least a little. If I HAD to have a couple of rounds to shoot out of my 32-20 and had nothing but 32 H&Rs available... i'd probably put a couple of wraps of tape or even paper around the lower portion of the case body and call it good. I wouldn't use this routinely, but it would be fairly likely to work, and if nothing else were available...
Then again, I have dies to reload my own 32-20s so I shouldn't have to resort to this. I was just trying to answer the OP's question about possibilities. In fact, back to his speculation, a wrap or two around the shell body of a 32 S&W might well work too.
Froggie