yes, they certainly could, but gaza would then have to deal with a turkish military occupation instead of an israeli one, and ask libya or cyprus or armenia about that. the turks would be unlikely to leave.
however, turkey would be unlikely to be much of a threat to israel, as well. they may turn gaza into a naval base, but that would just give american vessels in the region somewhere safe to park. it would give the palestianians jobs, which would be a major breakthrough (mass unemployment creates economic reliance on hamas).
it ought to be egypt that does this, but if they refuse to do it, and turkey wants to step in, egypt will have to deal with the long term consequences of it's own negligence, which it outright refuses to do.
the idea of putting the palestinian authority in charge is a non-starter. fatah is overwhelmingly unpopular. the palestinians themselves will try to overthrow them.
it's not a bad idea, really. it's up to the egyptians to make that decision.