Is management truly unaware? Or are they just hoping it isn't as bad as it seems while they stall for a better solution?

If you had to guess, are you more valuable to your MSP than this guy is? Are the other techs more valuable than this guy is? If he's not actually doing the work then surely he's not a valuable employee. Unless he's the owner's nephew... why can't you just go to management and tell them it's been long enough, they need to make a decision regarding this guy because it's him or you, him or the rest of the team.

Of course you can quit. Every employee has that right. But if this MSP has been at all good to you, or you think it is worth protecting, I'd try that first. After all, doing the one doesn't prevent you from doing the other. If you are going to quit anyways, why not try to fix it first?