I'll be curious to hear what others with more experience think, but my observations with persimmons is that they tend to be pretty tough plants. With that said, they also have a fairly prominent tap root, which might make them difficult to transplant without injuring.
I take it most of these were bare root seedlings when they were planted last year? I put some from MDC in a gravel bed to baby them and transplant them later. I would say they doubled in root size (compared to the above ground growth) in a growing season and I ended up snapping off that tap root. Depending on the growing conditions, they may have a similar size root mass as to when they planted. For what it's worth, I think the majority still did fine after transplanting from the gravel bed.