I dunno if Paypal calls you with a robot, when you add phone numbers. If they do, then you can't use a bogus phone number. But you could buy a cheap burner (cell) phone (I think that's what they're called) with cash, at a convenience store or something.
Well, if you set up fake shipping and contact info on Paypal, you can enter that in, on the forms, before you get to the part where you select to Pay with Paypal.