I wouldn't imagine they would. Cover it up and make sure there is at least one public entrance that doesn't have a sign. Oh, and stay away from MRIs...
I consider hospitals one of those fairly high risk locations. Think about it: sick and hurt people not getting treated as fast as they may like, both sides of the latest gang shootout lying feet apart in the ER, lots of really good drugs, and in most cases, VERY minimal real security. So I avoid going anywhere near a hospital without being armed.
That said, there are two very different circumstances under which I normally visit a hospital:
1-As a visitor to see someone who is the hospital;
2-As next of kin, responsible party, or "advocate" for a person who is receiving treatment.
In the first case, I don't much care if I CC or OC. Here in Utah I can carry as I see fit and the worst the hospital can do is ask me to leave. And I'm rarely going to be present for any actual procedure if I'm just visiting.
In the latter case, I conceal or even deep conceal. Not only do I not want to be told to leave when I am there helping care for a family member, but when someone is cutting into, stitching up, poking, probing, or otherwise treating my loved ones, I don't want them at all distracted or made nervous by my firearm.
There is a time and place for everything and when someone I love is being treated in a hospital and I'm there to help assure proper treatment is
not the time or place for me to be making political statements or "educating" anyone about self-defense.
Shopping for groceries or gas, watching a movie, reading in the library, eating out, or just taking a walk or hike or bike ride are great times for political statements and education.
Just my $.02 worth.
Charles