If I hired a man to do some work on my roof, does his signed document holding me harmless in the event he injures himself?

The answer is, "it depends":

1) A person can waive his or her  right to sue for ordinary risks of the activity; so, for example, if he falls without it being some fault of yours, the hold harmless should suffice.

2) However, it generally difficult, if not impossible, to have a liability waiver or hold harmless agreement insulate you from liability due to your fault. In a roofing case, for example, say that he doesn't fall on the roof itself, but on the front stairs to the home because of a loose railing or broken step which you never fixed--you could be liable for that. You could also be liable for his injury if he used a ladder of yours which was broken; if there were  hidden dangerous conditions on the roof (e.g. the rafter beams are broken, creating "soft spots" or hazards not visible from the outside); etc.

Therefore, you should probably not  hire him unless he can show you proof of insurance he has obtained for his own benefit.