The person I spoke with when I called was not the interviewer, but they immediately _DEMANDED_ to know who I was, why I needed it, what I was going to be sending, to whom it was going to be sent, why I felt it was necessary, etc. They then very hesitantly gave me the address after placing me on hold for a while. I probably should have just taken the hint and not sent them anything, but I went ahead and sent it anyway.
I never got called back. I don't write thank you letters anymore.
For a phone interview, I would definitely think it "noise", but it wouldn't be a significantly negative signal.
I'd tell your recruiter that you're looking forward to hearing from the company (assuming that's the case), but that you will reserve any thank-you emails for later in the process.
In fact two of the candidates were passed on simply because of what was in their letter, it didn't express enough of a desire to move forward and they seemed more like a resignation letter.
Be safe rather than sorry, and skip that unnecessary process.