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!

Same as what was said by The guru.
Apply your effects to the dialogue afterwards. A convolution reverb unit/application will be ideal.

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