Typically, coasters that are made of a non-absorbent material have a bit of a rim so as to contain the sweat from the glass. That would be hard to arrange for a PCB, but not entirely impossible. You could put a wire around the edge as people often do for a high-current trace.
However, I see more and more coasters that are pretty much just decorative, so why not.
Of course, even cooler would be a PCB coaster that actually did something. Maybe light up your drink and change color with the temperature or something. :-)