I actually have always played this with a relatively low mouse sensitivity and I've managed to do alright in this game.
I used to play a good amount of fps on consoles with my sensitivity turned high and could whip around a 180 at pretty much the same pace as I do now with my mouse in this game. That being said, the speed of a 180 turn in this game isn't nearly as critical as communication teamwork, strategy, tactics and positioning. I think console gamer's will do just fine.
No everything will. No way you can snap your view to a full 180 on the helm with a pad as fast as you can with a mouse. Engineering is similar with repairs. If you have to move fast and adjust quickly for repairs/extinguish, you can't do it fast enough with pads. It'll be playable yes but pad based teams will not be able to compete without either heavy tweaks to sensitivity or just giving up and connecting a mouse.