I'd be very surprised. It isn't even a given he'll become champion at MW never mind any other division.
I don't realistically see him ever competing above SMW but say Golovkin went up and the champs are Stevenson, Kovalev and Beterbiev is still looming. I see him going 0-3 against all 3. (yes against Stevenson as well)
I think GGG is too small for LHW. He could beat some guys, sure, but he'd accumulate damage at a rate of knots. He'd burn out in that division.