WAV, one of us (at least) is getting confused by this discussion.
If two people sing in the same key, either in the same octave or an octave apart, it'll sound fine. If they sing in different keys that are not an octave apart, and both go do-re-mi, they're not both singing in C. Doh is just a name for the first note of the scale, in any key. One would be singing in C and one in G (or one in D and one in F, or whatever) and it would sound awful. That's neither unison nor conventional harmony.

I really don't know what you mean about introducing a chorus on recorder and then changing the key. It sounds a disconcerting thing to do, and why would you do it?

Help me, someone out there! Is any of this making sense?

Marje