You would need to strike a balance between doing enough damage to build callouses, and not doing so much damage that you cut yourself (and build scar tissue). Scar tissue is weaker than regular skin, and can take weeks to a couple months to fully heal, and get strong again.
My somewhat related experiences
In rock climbing, there's a technique called "hand jamming", where you use your hands as wedges to climb a crack system. I have met old climbers out West (Wyoming and California) with crazy thick callouses on the back of their hands. So, I'd say, yes, it apparently is possible to callous up skin on different parts of your body (in this case, the backs of your hands).
Whenever I try and climb hard hand-cracks without athletic tape, I just scrape myself up, and get scars on my hands that take a while to fully go away. As a weekend warrior, I don't think I could duplicate the lifetime of climbing it would take to slowly build those calluses. I could probably devise a skin-training regiment I could do daily, or every other day, to toughen my skin up. But assuming my goal is to be a better climber, I have better luck just taping up, and working on my technique. (honestly, I think that's a better application of my limited training time).
I should say, one of the climbers I met was an old guide, who had thicker calluses on the backs of his hands than most people have on their feet. He also had long, grey dreadlocks. It looked weird, but kinda cool.