Can I damage a tubeless rim using a wire bead tire on it?
To answer your question in a word: No.
You can run any tire on the rims you want. The "UST only" sticker is referring to when you're running tubeless. Even then I wouldn't pay it much mind. There are plenty of good non UST tubeless tires out there. Squirt some sealant in there, air them up and off you go. The UST standard is a dying (dead?) standard. Our friend Stan played a big part in making that happen. Before there were many tubeless tires available his tubeless kits converted most, but not all, non tubeless mtb tires to tubeless with no more issue than you would have with a UST certified setup. Some would argue that the NoTubes kits were more dependable than UST.