It depends what your idea of "big" is. You may be able to get "big" in relation to the size you are now, but not big like Ronnie Coleman, even without the juice. Same goes for strength. The point is, even with poor genetics for muscle building, everyone can see satisfying results with proper diet and training, but it takes time - a good four to five years to reach your peak physique, and even then there are always small improvements to be made. This is usually the point at which people start trying steroids. But don't start thinking, "shit, I don't have four or five years to get big, I want it NOW!" There's no instant gratification when it comes to BB, but you will see constant results and improvements, which will motivate you to keep working.
peace
TOkidd