I don't think so, though anything is possible.
Based on his size and the features on his face, I'd say if anything he might have some sort of gigantism. This alone would provide a higher rate of GH.
I only say this as I've seen guys at the gym years ago who were on GH and their facial features seemed to change, plus many years of reading muscle mags. Just a hypothesis, he could just really be a big guy who became an athlete.
To be his size and have such coordination to hit a ball as he does is quite rare. Andre the Giant had full blown gigantism and he was quite uncoordinated.
When I saw Jason Giambi play live for the Yankees, with good seats behind the plate, I saw the shape of his back when he was on the on deck circle and looked at my friend and said almost incredulously "that guy is on juice". Shredded, striated forearms with massive back development. He promptly hit a HR that AB. Years later he admitted to doing so. He was far from alone of course but it's much easier to determine in the flesh.
I don't see the hyper muscular development in Judge, just a very large structure. He may not even be a powerful lifter in the gym, just a large man with a high leveraged powerful bat.. TBH, when I look at Stanton and his massive legs and glutes, I would suggest HE would be more the probable user.