If you were convicted, it WILL show up and it is also a felony to attempt to purchase a firearm if you are a convicted felon. So be sure before you have a dealer run a background on you.
You need to ask an attorney this question. It will certainly vary from state to state as to the procedure for reinstating rights. I will say, that I know a couple of folks that were successful in my state,with one having been made whole very recently...took them the better part of 20yrs to get it done, but there convictions were not 43yrs in past, when they started the process. It will most assuredly be a slow go in any state...and not inexpensive.