I need to mount a projector shelf, however finding a stud is proving impossible. Is it a terrible idea to put this shelf up on drywall and then the projector which probably weighs at least 15lbs?:
Do (or will) you have kids that will want to try to do a pull-up (or sit on) on a convenient shef?
If not, then using the proper anchors should be fine. Many anchors will support far more than the weight you indicated (which is good, due to the leverage the shelf will place on the mounting points.
I'd look at toggle bolts instead of screws or thin plastic plug-style anchors to be sure the projector is solid. The holes are large, but will be easily patched when you decide to move things around (eventually).