No, they won't. If you don't give them a video signal, they won't know what to do. The PwerMid approach is designed to deal with remote control signals, not video (which requires repetition, particular voltages for sync, etc etc WAY different from an IR signal).

Apparently the PowerMid takes the IR and does little to it before sending. Therefore the downstream PowerMid does very little to the RF when converting it to IR. This second thing is the ideal situation for converting an RF command to IR.

Now the only hitch is that the IR output of the PowerMid has to be in a form that the remote can learn. Mistakes were made with the first New Generation Prontos, and perfectly good IR codes could not be learned. If the pulses or whatever in the RF commands are just too way out for the remote to learn, well, then you're stuck with no solution.