Well, no, let's think about it a little more than merely briefly. Let's assume the feeder fish has been dosed with a carefully measured amount of anaesthetic that is appropriate for the size of the animal. This alone is a huge assumption, but let that go for now. So you have a thoroughly doped-up small fish which is then fed to your predator. Perhaps you feed it several such fish per meal. If you feed the fish twice weekly, the predator will ingest all that anesthetic from all those feeders...and this will continue on and on, for weeks, months, years. I must further assume that an anaesthetic used for this purpose will not accumulate within the tissues, but will rather be processed and metabolized out of the predator's system, which of course is a good thing...but you are continually dosing, dosing, dosing...
It sounds like a typical drunkard's vacation. Maybe never actually drunk...but always with a low-level buzz that is maintained by a steady intake of alcohol...or in this case, anaesthetic.
Oh, what's that? You plan on feeding these sedated feeders only occasionally, using them for only a portion of the diet? In that case, why bother at all? If your predator really requires live food...and that is a tough notion to sell!...then you will either be forced to feed a bunch of prey items that don't contain the anaesthetic...or you will manage to train it to feed on other, non-living items as well. And if that's the case...why would you
ever feed live?
There are, of course, those who feel that it's cool to feed live animals to other animals just to satisfy some atavistic sadism. The more gore and violence, the better. Just google "piranha feeding" if you want your faith in humanity crushed.
I'm thinking about it from the viewpoint of one who eats a lot of meat, and almost all of it is procured through hunting. If I believed that there was a realistic chance that the deer, moose, whatever...had been sedated at any point in its life, I would give it a pass and look for another. Of course, one can't be 100% certain...of anything...but for sure, an animal with a tag in its ear, a number painted on its side and a dart sticking out of its ass end will not end up on my dinner table.
I'll bow out here. This thread started out with what I consider to be an unrealistic and impractical idea...and now it's begun to spread to include abortion, fascism...not what I or, I suspect, most people come to an aquarium forum to read. Enjoy!