In theory, yes: you will be a, presumably, board eligible/certified IM physician, so you'd be able to do outpatient or inpatient general internal medicine.
Though gutonc poses a valid question: "why?" Most people do fellowships in order to earn more money or to get a better lifestyle (or, in some cases, because they dislike primary care/general medicine). I personally, have not seen many GI, cards, or heme/onc guys doing much hospitalist or primary care work... probably because they can make more money doing something else... though, in fairness, some general cards guys do a mix of IM and gen med. Also in some academic institutions, subspecialists sometimes attend on the wards with residents, though with the large expansion of academic hospitalists, that is getting less common.
For other specialties, I've seen quite a few endo guys do a mix of outpt endo and IM to pay the bills and have also seen this in rheum and ID. It seems difficult to do pure endo here and keep a roof on the house.
For nephrology, I've seen quite a few nephrologists working primarily as hospitalists and some do a mix of neph and primary care (also, rounding on dialysis patients often leads to primary care issues being brought up). Again, they usually do a mix of stuff because it may be difficult to make a living as a pure nephrologist in some areas.
Some pulm guys also do a mix, but doing ICU shifts pays more, so its not as common.
All of this depends on your practice setting, geographic location, and how much free time you have to do other per diem stuff.
People tend to do what maximizes their salary and/or improves their lifestyle.