The only time I can think of that a CHP holder could not sit at the bar area is in certain establishments where there is a separate bar area that has a difference license and that license is not a Class A Restaurant license. I can't remember where it was but I went to a restaurant one time while working and there was a separate door that had under 18 not permitted on the door and it led to the bar. In that case, I would think through the door = not legal.
If they don't have a Class A, you can carry and sit at the bar. (Applebees, Chili's, etc).
It only allows commissioned peace officers to carry in a Class A.