Yes, it is possible for a general surgeon to do mostly hernias, gallbladders, etc. This will differ greatly from surgeon to surgeon depending on the hospital and other practice settings. It really depends on the town you are in and what other surgeons around you are doing. But it is possible to work at a smaller hospital, say, where you do a few hernias, a few gallbladders, one or two breast cases, or maybe a sigmoid or so a week. But there are also some general surgeons who are the "only game in town" and who do some gyn, some ortho, and some vascular stuff, in addition to the hernias, appys, gallbladders, etc.
Also, as fishmonger said you do not need a Peds fellowship to do basic peds cases like hernias or pylorics, as long as you have significant numbers and exposure to these cases in your residency. But someone who has not trained in Peds would not/should not attempt do more complex peds cases like a Nuss bar (for pectus excavacum) or congenital diaphragmatic hernia repairs.