ohhh man this is a good question BUT i have to warn: it's not very nice. so if you only want positive / fluff readings of the two, i'd skip this one ...

baldi only really cares for the game, and i feel like the principal is aware of this.
he's aware of a lot of things. he has to know when one is breaking the fourth wall to be able to enforce that rule, so he has to know at least something about the game itself. and i can't imagine he's ignorant to the way baldi thinks about him.
everyone in the school is only a part of the game to baldi. take baldi's tips'n'tricks'n'lessons (which is also one of the very few places where any character acknowledges any other characters, so if that interests you, read it). when he speaks about playtime, he recommends staying away from and keeping her from seeing you at all, because she's just part of the game. for the principal he explicitly says "Follow the rules... but only when the Principal is near!" because, in his eyes, the school is not important. the people in the school are only obstacles for you to overcome. i have not found any reason to believe he cares about these people outside of their game functions.

with that established: for baldi and principal to have any emotional investment in one another, it would not be a very caring one
baldi doesn't respect the guy's few explicit values. go behind his back and do it while he isn't looking, he says. great foundation to build a relationship on /s! even if he did care about the guy, secretly, without my knowledge, baldi would still not truly Respect him, and so i can't imagine him being in it for anything other than his own gain. especially since i do not think the principal would really love him back. he'd only be in the relationship for the structure it provides, same as his whole job.
the principal does not care much about the rules. he hardly punishes for them, only a measly handful of seconds for even the most adamant of offenders. and he never takes the context into mind, either, he doesn't care where you are or what you're doing. he doesn't care about what the Rules are, and more that there Are rules. he needs to keep some kind of order, no matter what that order is, and without it he'd be nothing. he has a passivity and emotional dullness that i can't help but think of as depression, so this makes sense. get a job to keep yourself from falling over. be around a man who wants you for something even if that's all you are to him. at least you're wanted. at least you aren't rotting away somewhere. he enters a loveless relationship, knowing exactly what it is, knowing he is just an item to the other party. his whole role is knowing that he's nothing to baldi and still keeping up his duty because he can't bring himself to care.
baldi, i think the second he's rejected he would back off. if the principal said "no, i don't want to do this," he wouldn't fight against that. he doesn't seem like that sort of man to me, at least not to the principal. but the principal just wouldn't reject him. because he only says "no" when it's already written down. he only cares about his thinly veiled idea of order and structure, more than he cares about even keeping the veil over it.

this issss... all hypothetical, of course. baldi would have to make the advances, which is the largest barrier because i can't really think of a reason why he'd do it. again, he only cares about the game and maybe whatever contract he's under (if any) and so i don't know why he'd go enter a relationship with someone...? but if he did, you know, that's what i think of it.

in short: princibaldi to me would be a relationship where both sides know it is false and yet they continue. the only love here is love of the game