I recall reading (Mishnah Brurah - don't recall location) that the shali'ach tzibbur must wait until everyone answers "amen" before proceeding to thE next bracha. If a deaf person were prompted by someone else using a signal, would this allow him to be a shali'ach tzibbur?
See Siman 55 in Biur Halacha: http://www.hebrewbooks.org/pdfpager.aspx?req=14170&st=&pgnum=172&hilite=
Summary: Taz isn't too fond of the idea of having a deaf Shaliach Tzibbur. If he is davening, however, according to Magen Avraham, Gra, Bach and others, it appears we should not remove him from the amud. Rabbi Akiva Eiger concludes that l'chatchila everyone would agree he should not daven at the amud.
EDIT: To speak to Shmuel's point, deaf people have the same level of obligation provided they can communicate verbally. See Shulchan Aruch in same siman.