Honestly, I have no idea...I haven't had my spare tire underneath in a LONG time. Even if my spare SSR would fit up in there, it would probably be touching the exhaust pipe, which would be a bad thing...
I remember talking about this with someone long ago, right when Synchro first got his KMA...not sure what we decided, though.
Sorry I can't help you...I do know you lose an inch or two of space, about what you do w/ the Nissan hitch methinks. So maybe say a normal 32 is a VERY tight fit, 31's will fit okay, and 32+ sized tires (like 32" SSRs) won't fit at all.