Not really, especially not with this fan. At least, not on the fan. You would need one on the relay, but your module already has it on its little PCB. It's right next to the relay.
Back EMF protection and crowbar protection are completely different things, with different implementations and to deal with different problems. They have nothing in common except that semiconductors are in there somewhere.
Good news 
2n7000 is a common type, which is why I mentioned it. In case you can get BSS138, that's also a very suitable one - even better, as it's a logic-level type which is more suitable for an Arduino environment (to put it simply). The problem is that I think it only comes in SMD form whereas 2n7000 is a convenient TO92 package.
Yeah, they're cheap and often useful. It's always a good idea to have a dozen or so (or a hundred...) on stock.