Auto processing would certainly be possible - but it's a lot more complex than auto-sell, or infinite manufacture; because unlike those other things, there are are several micromanagement decisions which need to be made by the player in order to process the prisoners. For example, how many runts to assign, which current process to remove those runts from; start immediately, or wait until current projects are complete, etc.
Because of this, I don't expect auto-processing of prisoners will become a feature any time in the near future. It would be a significant amount of work to implement, and it would be potentially difficult to integrate into the UI in a useful form. So unless there are other major automation features added to the manufacturing system, I don't think auto-processing of prisoners will happen.