Your summation of what I wrote is basically correct, although by 1864 most recruits werent sent to "training camps" but directly to the forward areas for dispersal to their then assigned regiments. A replacment soldier most likely got his training from his new unit.
Camp Dennsion I believe was being utilized as a training facility for new regiments being raised in Ohio at that time. As a rule, Ohio enlistees would be assigned to Ohio regiments. The exception to that could be West Virginia regiments, as many of those units were filled with Ohio boys. I dont know if later recruits from Ohio were ever assigned to those units.

As to your possible ancestor, do you know when and where he died? If here in Ohio, there are sources that could help verify his service.

Kent Dorr