University Philosophy? I'm not an expert in university philosophy curricula, but I'll speculate as follows: the AOTC would show up somewhere in the curriculum but is unlikely to make an appearance in an Introduction to Philosophy subject. The AOTC has an entry in the Internet Encyclopedia of Philosophy, the Stanford Encyclopedia of Philosophy, and Britannica.
Plato's cave? No.
Has anyone said Existentialism yet? No.
Is Existentialism the AOTC? No. (I'd put that more in the vicinity of Spiritualism on the M-m scale.)
Does it entail a belief in predestination? You just had to ask that, didn't you? No.