chirp spread spectrum with 2 users
Yes, you could. When you're using spread spectrum for multiple access, what's important is the cross-correlation between any two users' spreading signals. Any cross-correlation between two users' spreading sequences will cause "leakage" from one user's channel into another's; this causes an artficial noise floor that will limit your system's performance.

You'll find that an up-chirp and down-chirp have very little correlation with one another, so they would be usable for this purpose.