i bred rabbits for more than a decade (mostly to use as falcon food), at one point we had more than 100 running round the garden. we used to feed them lots of lettuce, we'd buy a crate from the market and dump it in the garden, it gives them runny poo but they liked it and we never had a single unhealthy rabbit.
i think being torn apart by a bird of prey (bravo!! by the way) is more on the minds of the little furry butt lickers than the contents of their bowels, which either way will be spread across the countryside........
they were always killed humanely before they were fed to the falcons, you cant release live domestic rabbits for falcons because they dont run away so its boring for the bird and it wont get enough exercise. we used rabbit meat as food when hand feeding, live bait was pigeons and kirowan (a kind of desert pheasant)