Not very good I'm afraid.

Singing in the bathroom adds reverb, a sort of echo. It makes the sound "smoother", the audio equivelant of a soft-focus filter. Also it tends to add more echo in the lower frequencies than in the upper, giving a nice "round" sound.

In voice-overs you (usually) want clarity, rather than an echo.

Also, you can always add "reverb" or "echo" in post-production but you can't get rid of it once it's been recorded live.

Good idea though!