I did try this, and I can still tell. I sent someone a voice message, then told them to re-send it to me at a random time. Could still tell it was me.

I did, however, get around it while voice training? I’d spent a week speaking in a different voice to my usual, then when I recorded something in my usual voice it didn’t give the effect you usually get when listening to your own voice. I did get it when listening to a recording done with the trained voice, though.