Looping 12G SDI through Studio Fiber Converter?

We've just upgraded our multicamera field production system, adding two URSA Broadcast G2s with fiber converters and an SDI URSA Mini 4.6K Pro. I just realized I am short of 12G SDI outputs to provide remote control (shading) from the ATEM to all three cameras. Can I loop one program signal (Return Video) through the two encoders and then on to the URSA Mini so I don't have to beg for funding for a 12G DA? None of these cameras actually need return video feeds, just control.
If I route Program Out to one of the Aux outputs, will the control signals be available there?
Thanks,
Ric
If I route Program Out to one of the Aux outputs, will the control signals be available there?
Thanks,
Ric