It's possible if the core isn't sealed to the bulkhead, but for any OEM installation the fan can be completely removed above 35 mph.
My sister borrowed her boyfriend's car (Mustang L4, 4-speed) for some errands in Jacksonville. After a while it started to run hot, so she pulls into a station.
The "mechanic" pops the hood and tells her the problem - "hey, lady - your fan came off".
Boyfriend removed it, since he never drives the car in traffic, and never told her.

BTW: lest you think he's just some local grease monkey - he's Racer Walsh.