Never tried it, but it can't hurt to anneal it. I'd assume that it would work-harden at least a bit when struck, and be left that way for durability while in circulation. If it is a 20th century US dollar (i.e., Morgan or Peace) it should be 90% silver and 10% copper, per Wikipedia. Same with the half dollars.
More random research that may or may not be of interest:
Early U.S. Federal dollars seem to have also used that 90/10 ratio, so it would by authentic for a repro of that era....Spanish dollars were theoretically 93.05% silver up until 1728, 91.66% silver from 1728-1772, 90.28% silver between 1772-1786, and then 89.58% from 1786 up through 1821, so roughly equivalent as well (the Spanish dollar was a common coin in 18th century America, I believe, so a likely donor for a coin silver inlay on a rifle of the time.) No word on the alloying elements. English shillings, as far as I can tell, were at least nominally pure silver up until 1816, when they went to around 92% silver, but I have to wonder if that was really the truth.