There are several previous posts on the subject of fellowship-trained docs doing general ENT.
But I will make a couple of points. If you do a fellowship to get into a saturated market as a specialist, you're going to be hired to do the specialty stuff and not general--except perhaps on call.
If you do get in as say an otologist, and then want to do sinus stuff, all the docs that referred you ear cases will dry up rather fast because they'll see you as competition for their practice, not as a resource. Bad business decision making in that arena.
I know several docs that have fellowship training who do general. Often these are people who just wanted to have a better understanding of that particular area, often because they didn't get good training on it in residency. But they don't bill themselves as the "ear guy" or the "sinus guy" or whatever. Most of the time they don't even mention it. Now, I do agree with neutropeniaboy that it is probably not really financially worthwhile to do a fellowship to have a general practice.
As a solo ENT, you can be quite successful in general and miss one and even 2 areas. In other words, you could be in a general practice and not do ears or head and neck cases and still do well. Missing out on 1 area is not going to affect your bottom line, whereas missing out on 2 could depending on your practice setup. Missing out on more than 2 definitely will start to affect your yearly collections IMO. If you're in a group, missing 2 or more doesn't affect you as much because you can usually have your niche, but your partners may not necessarily appreciate it esp if they're doing some of the grunt work that you won't take (i.e. trauma).
