Ideally, the expert who fits your fiancé for his tux will do an excellent job and you'll have nothing to worry about in terms of fit and function. If it'll make you feel better, consider sending his mother or another trusted person along when he picks up his wedding day ensemble. Have him try it on in the store to make sure that everything fits, his hems fall in the right spot and that all of the essential accessories have been provided.
Typically, a standard tuxedo rental will come with the pants, shirt, jacket, cummerbund or vest, cuff links, tie and shoes. Be sure that he checks his inventory in advance! If there is a problem, he'll have time to sort it out with the store. So, as long as your groom has underwear and socks, he should be in good working order for the ceremony. Remind him kindly that underwear is not negotiable. It's just not kosher to go au natural in rental wear. The tux's future wearer will thank him.