Why not? Carp are one of the most eaten fish on the planet. And, honestly they are quite tasty smoked, best time for them is early spring before the shallows warm up a great deal. Up to about 6 - 7 pounds is best, beyond that they get a little big to smoke whole, and you have to steak them out.
Have also grilled them early spring, little seasoning salt, lemon pepper, lemon juice and butter to baste. And, they were quite tasty. But again, this was early in the year before the shallows warmed up, and it wasn't a real big carp.
Typical recipes for larger fish would suggest boiling them in a court bouillon, then flaking the meat to make fish cakes or patties. If you go this route with larger fish, trim the darker flesh along the lateral line from the fillet before boiling. It harbors most of the heavy oils, and likewise toxins from run off into the lake/river/stream.
Older compound... Mine was a Bear - Black Bear II. Boat is cool, but wading is a blast, and much more affordable. You can get right up in the middle of them, have fish bouncing off your legs and feet as they swim through, it's way cool! If you're thinking about wading, look for a bow with short limbs. It allows you to get deeper and crowd the fish to shallower water for shooting. Been down the handwind reel route, and you couldn't give me another. Used a stubby rob screwed into the stabilizer hole, and a Zebco 808. Allows for much quicker recovery on missed shots, and thus more opportunities to shoot before the school passes.