I don't know if giving them the oyster grit necessarily will INCREASE egg production....they are pretty prolific layers anyway....but it will keep it from decreasing from a lack of calcium, and it will ensure that the eggs have a solid shell. They aren't "year round" layers like production chickens are, but they seem to lay quite steadily through the normal laying season, from spring into mid-summer, at least.
I have all of my chickens eating a diet of cracked corn, supplemented with either the granular layer's mash or the wild game (pheasant) feed during the laying season to keep them in good shape....even the roosters need it since they spend most of their time chasing the hens around they yard and can actually get pretty thin themselves. I also keep a fine cherrystone grit available at all times, and also give them the oystershell free-choice during the laying season.
Contrary to what people think looking at these tiny birds, they are a very hardy breed, and don't really need a lot of "special" care as opposed to a plain old chicken. The roosters do tend to be a bit more ornery towards each other than "regular" chickens.....I always kept mine caged in breeding groups to keep the roosters from fighting, as opposed to my other chickens who have the run of the whole farm, lol....but toward humans, they tend to be very mellow and less flighty than other chickens.....my kids had several "pet Pyles" they would pick up and carry around all the time.
One thing you may notice is, depending on the breeder's preference, some will still "dub" the roosters.....meaning they remove almost all of the comb and the "wattles"when they are young, the original purpose of that being one less thing for other roosters to latch on to in the cockfighting ring, and the tradition kind of stuck even now when most people no longer raise them for such an awful purpose (kind of like ear cropping on pit bulls, for example....eeesch). I kept all of mine natural, and think they looked beautiful with the big combs, however they did tend to freeze the tips in a particularly cold winter here in Iowa if they didn't have heat lamps.
If you like the Red Pyles, you would also really enjoy the Silver Duckwing old english game birds. They are very similar, but the colors on the roosters are quite striking.