Certainly, with analog SD there would be no way to even tell the Tv that the signal was originally in 24p, because there was never any standard developed for the overscan line information to encode it, and it couldn't project the signal that way if it were a CRT model. Only front projectors of the analog type could do that, so what would have been the point? digital Tv's can do it, but to what point?
The TV doesn't even need to know. It wasn't necessary for standard tube TVs, but it really helps with HDTVs.
The deinterlacer chip analyzes the picture, if it detects that it's a film source, then it does all that work to correct the video. Sending incorrectly flagged or unflagged video is one of the torture tests that can be applied to such a chip. I don't know what they cost now, but a good chip was $30 a few years ago. A Vizio and such probably won't have anything like it at all, but the more established brands are more likely to.