Reversing headset speaker to microphone
Yes.  Back in the day, we used acoustically coupled modems that you sat the telephone handset in and that was fine.  For DTFM, in particular, when many phones were still rotary, there were things like hand held speed dial devices where you just held the small speaker up to the handset while it audibly produced DTFM tones.  DTFM algorithms in both hardware and software are pretty robust.