yes, you could, and that would be a sensible place for the origin.
you could put the origin anywhere that makes sense for your situation.
a “flat board” would make sense if any of the markers could be occluded. then recovery is still possible from a complete view of at least one of the markers.
if occlusion is not the issue, but noisy rotation data from a frontal view is the issue, such a flat board has no advantage over a single marker in the same plane. it’d be better to have the “board” be 3-dimensional in some way.