I'm pretty sure I've heard that they can, I have no source for this though. I wonder if this is linked to phenomena such as spontaneous degranulation in the complete absence of an antigen in mast cell disorders (once again, not positive this is a thing, but I believe it is).

Though on that last point IIRC, I believe I've heard it also just has to do a bit with random conformational noise on the receptors causing autoactivation.