IIRC, you can complete the SSE, but you just can't use any character past DK, Mario, and Link. This is because Samus is next in line to be unlocked in SSE, but Samus isn't available in Demo 2, so it prevents any other characters from being unlocked.
I'd assume the giant fake Diddy Kong freezing would be because it's trying to load Mario.
Has anyone had a freeze when playing Boss Battles? I haven't tried it in Demo 2, but I froze a bit a while back.
I don't like BtT that much in Brawl/PM because the stage parts and targets are too far apart to be able to do a riddle challenge. Also, IIRC, you can't unlock certain target test level settings because you can't play all characters.