Don’t know if there’s a source of “new” comets, so yeah, if one is seen hitting the sun, there’s one less.
Tunguska, if it was a comet, took out one more.
The number of comets discovered, though, is holding about the same since NEO and NEAT and the near-Earth projects started. David Levy had visual the comet discovery title locked up until the US launched the IRAS telescope, and that sat was used to discover scads of them.
Comets move in from Oort and Kuiper belts due to tidal and orbital instabilities, some are detected optically, I’m sure that there are some we don’t see (since IRAS could see lots that we had missed).
http://www.asahi-net.or.jp/~zs3t-tk/comet_hunter/comet_hunter.htm
Here is an article discussing the hobby of comet hunting, the old way of visually finding a comet and reporting it (and getting your name on it) is being replaced by automation and modern observing techniques.