I can vouch for this. I used to have an FM system - this is a mic that transmits on a very specific FM frequency to a receiver that's paired with my hearing aids. I loved it because I could easily use it to hear people near me in loud rooms, but it sucked in meeting rooms. The reason why is that I would hear someone speaking through my hearing aids and through the mic - at slightly different times. This is the phase shift Dwolb speaks of. This reduced clarity significantly.

That said, if analog31 wants to wear the mic on his shirt, that distance is actually good enough for most 1 to 1 conversations. Just understand that you're trading off "spatial perception" (no left/right balance if only one mic).