Looking at databases I find a Samuel Martin 20 b. abt 1900 listed in the 1920 census in parents household (Samuel and Carrie) in Union County NJ. His occupation looks to me to be "Calvary, Private, USA". This census was taken Jan 5 and 6.
In in a 1920 census taken January 25th and 26th at Ft Myer, Alexandria County VA is listed a Samuel B. Martin age 20 solider, US Army. born in PA parent PA.
According to a family tree the citing the 1920 NJ Union Co census as a "residence" for a Samuel Bitzer(Betzer?) Martin, with parents Samuel Martin and Carrie Bitzer.
If this is who you are looking for then he must not have been deaf till a later age. He also would not have a Draft Registration card if already in Military.
Yes, if he was not in the military, even if he was deaf he would have had to file a Draft Registration Card and on it would have noted any disability he had or felt made hm ineligible to serve in the military.