If *everything* goes, yes it would plummet like a stone. However the chances of a complete systems failure are so slim.
In actual fact about the only way it could happen is due to combat damage, specifically being riddled with lead, in which case the pilot would probably be shot to pieces as well if it has knocked everything out.
Otherwise it would be a missile, by which time the pilot should have ejected anyway.
And Lee, pilots really shouldn't fiddle with their bits like that. Leads to premature ejeculation.