My first thought was "yes, it will". A smaller ROH has a deeper center, and the edges are thinner - wearing faster. Also, power sharpening could possibly remove the temper from the steel at the very tip of a narrow edge, leaving soft steel. There's not as much steel behind an edge with a small ROH to absorb heat from unlubricated power grinding.
Then I drew the blade's hollow to scale comparing a very aggressive 3/8" ROH to a gentle 1/2" ROH. They don't look nearly as different as I would have expected...
Having seen that, I now expect that outside variables would matter much more - hard vs soft ice, deep edges vs upright skating, clean skate guards vs. not, etc. I predict that it's a case of the theoretical being swamped by larger environmental factors.
10 hours between sharpenings seems like an aggressive schedule, and will reduce the life of the blades. At typical metal removal rates of .005" per sharpening (power sharpening), you'd remove a whopping 1/4" in one year skating @ 10 hours/week. However sharpening frequency is a personal preference. I'd just do what feels OK, so when you start sliding a bit more than usual, get them sharpened.