Hi Glenn,
Welcome to the forum. Nope, as long as the headers are meant for your 82 Corvette there shouldn't be any issues as long as it is relatively factory. If you have any upgrades like new heads with angled spark plugs you may have issues with not enough clearance by the spark plugs. I've found that you have to install them from the bottom up as you will not have enough room to install them from the top down.