It's been construed as an EMTALA violation. You absolutely can't and shouldn't be telling anyone what the wait time is out front, or the hospital is opening itself up to an EMTALA violation, which will bring down the pain of federal oversight into the ED and hospital to an uncomfortable degree. Once they have a reason to investigate the hospital, they can look at EVERYTHING you do. Best not to get smacked down by the feds in the first place.
You can post wait times on a billboard off hospital grounds, because that's an advertisement targeting people who have yet to present to the hospital. Once a patient presents to the ED, telling them anything that would disuade them from waiting for a medical screening exam (MSE) is an EMTALA violation. Not only can you get slapped with a huge personal fine that insurance doesn't cover, but again it opens up the floodgates of investigation.
Now once the patient has a MSE, say from a midlevel or doc in triage if your hospital operates that way, you can tell them whatever you want assuming they've been deemed to be without an emergent condition needing stablized by the MSE.
Another example of this that has come up recently is ED pain guidelines. If an ED adopts a pain policy restricting narcotic prescriptions for chronic pain (ie, we won't refill your script, give you a shot of dilaudid for your chronic pain, etc) and has the local paper print a story about their guidelines, or takes out an ad announcing them, that's ok. If the same ED puts a sign in the waiting room where patients can see them before getting an MSE, that has been construed as an EMTALA violation.
It all has to do with what the patient is told in the period after they present to the ED, but before they get an MSE. What is announced to the public who hasn't come to the hospital, or what you say to someone after they get an MSE and are "stabilized" is all fair game.
Hope that helps.