Yes, you can do a hand fellowship after general surgery.
If you use a FREIDA search of "ortho" hand fellowship programs and read the web pages some/many of the programs you will see that the requirement to enter the fellowship often includes board eligibility in general surgery, not just ortho/plastics. If you look at the fellow profiles, you'll see general surgery guys mixed in all over the place.
At the same time, in a recent ortho conference, there was mention that hand fellowhips are going to have to incorporate more upper extremity into the training programs; I don't know how this would effect general/plastics guys, at least in ortho-based programs (whatever that means). From an ortho perspective, hand isn't the most popular area to specialize in.
Generally speaking, if you want to do a hand fellowship from general, you will probably get in somewhere. It certainly wouldn't hurt to do some hand research in residency and would certainly be necessary to hit the ground running in fellowship (ortho residency includes a lot of hand education and experience). Hand mechanics gets very difficult real quick...