The mon can be transferred into SWSH (via PKHeX) just fine without a HOME tracker.
If you're talking about transferring into HOME afterwards, in order to acquire a HOME tracker, I don't know how HOME will treat it.
Previously, HOME just assigns a new tracker, no questions asked, but it is unknown if they keep a long chain of tracker changes.
If they do, it can be seen that your first entry point was in Sword.
Anyhow, if you don't want a bad egg to be stuck on your present HOME account (if it does become one),
just start up Pokémon HOME in a new user account on the Switch (will also probably need a new Nintendo ID linked to it).
If it does become a bad egg, at least it won't be stuck on your main; it'll be stuck in the disposable alt :3