trouble outputting to video board

I have a ATEM TV Studio, Web Presenter, and OBS software that we have used to stream multiple cameras and loaded media, but now we also need to send the feed from OBS to a video board as well as a live stream. It was my understanding that the Web Presenter's SDI PGM OUT will do this... if I connect an SDI cable from the PGM OUT of the Web Presenter, to the SDI IN of the video board, will it display what I am seeing in the Program panel of OBS? Or will it only display the feeds coming from the ATEM TV Studio? Basically I need a solution to broadcast the OBS program window onto the video board. If I output HDMI from the laptop, it obviously shows my entire screen, and there is no option within OBS to output only the program monitor to HDMI. I thought this would be a simple thing, but am I wrong? Or maybe missing something?
Thanks!

It's program output, so it'll show what ever source is 'active' in the webpresenter at the time.