I’m currently playing through Pokemon Heart gold trying to get to fuchsia so that I can transfer gen 3 Pokemon to the switch. I also want to hunt a shiny Ho-oh however I want to get to fuchsia first, if I beat Ho-oh instead of catching it will I be able to rematch and catch it after I beat the game?
If you defeat Ho-oh, you’ll get another to catch it after you defeat the Elite 4.
Source and a lot of other places and experience and logical thinking.