It might work, but I can't remember if it's single-mode or multi-mode fiber.. It might not really matter though. My own limited experimentation has been with single-mode fiber, but I suspect multi-mode fiber might give you trouble when you collimate it.
The reason the beam wont collimate is because, in relation to laser fiber, that fiber is probably HUUUGE. I have a fiber coupled HeNe here and I've fitted an aixiz lens on the end and it collimates it perfectly. You just need some smaller fiber