In the early days, SIPP memory just plugged right into sockets with a friction fit, and tended to migrate out even in desktop computers that were never moved. Apparently the hot/cold thermal cycling was what gradually worked them out, and SSDs run much hotter than those. So the later SIMMs with latches were a great advance, particularly for laptops that get banged around.
I don't think there's any way to insert a M.2 sideways enough to short anything so it would probably be safe to run it screwless for months, and even if it popped out, you would know right away and could just pop it back in.