A 12v fan will probably work off 5v, but there're no guarantees
Personally, I'm against unplugging anything if you don't have to - two reasons.
1) There'll come a time when you forget.
2) There's a chance you might replug it wrongly, each time you plug it back in.
Another thing - the 5v pins on the GPIO header aren't GPIOs, and the GPIOs aren't 5v.
Just a matter of nomenclature, and unimportant in the grand scheme of things, but getting it right could avoid someone else getting confused.
And finally, while a motor (in a fan or elsewhere) is inductive, and so can create a reverse voltage when you stop the current through it, it also has mass, which acts like a capacitor.
When you remove the power source it'll keep spinning and provide 5v for a while. That shouldn't hurt anything - it'll just keep the Pi alive for longer than you expect.