I know that the original question was whether the sign is legal, and I agree with others that it does in fact appear to be legal.
At the risk of taking the thread off on a tangent, I am curious on thoughts as to whether this sign, as described would comply with the requirements in section 30.06 such that it would be legally sufficient to preclude the rights of a CHL holder to carry concealed on these premises. I realize that this was not the subject of the OP, but I think it is a valid point for discussion.
Given the scenario described, it is entirely possible that I might enter this hospital behind several other people such that the door was open (and the sign was not visible) during my entire approach to and entry into the building. It seems very wrong to charge me with a violation of a sign that I never could have seen.