Yes, but I would suggest a pile of cards. Either at the start of the draft/deck building/game a card from the pile is revealed. That way weird interactions will arise. Makes building the cube much harder than just one card though.
Having a pile of cards kinda changes the calculus, though. Part of the idea behind "emblem cubes" is that you're going "OK, you can all reliably build around [card] - how do you evaluate cards in light of that?". Ideally, you're making it so drafters have to reassess their rules-of-thumb and actually consider
why you decided to include each card... but I'm too much of a hack to pull that off.
You can't pull that off by making the emblem card
multiple choice. Or, if you do, you've expended more effort in the design experiment than you would by just building a mini-cube around each of the cards you picked. And the thing about weird interactions is that that's already what you're designing into the cube by making it
about a given buildaround.
I think this comes down to something I've talked about in the past - there's an
urge to maximize replayability in the cube community. Which is nice and all, but sometimes that doesn't really fit with the other stuff you're playing around with. Like, sometimes you make a mono-color cube because you're experimenting with signposting and not because you think that everyone is going to want to play the Monochrome Cube every single time you run cube night (though, hey, if that's what you guys are into, I won't stop you!)
...
I do agree that making it a choice of cards to build around for the challenge would probably be for the best, if only because it reduces the chance of accidentally picking a card that you can only really take in one direction. One of the best parts of
the 360/100 cube challenge/contest was that all of the entries were
kinda weird, after all.