(NYC)
My little sister had a bad fall yesterday and parents had to take her to the hospital at NYU Langone.
There was NOONE in the waiting area, and they were seen promptly.
The only difference: They had to answer a few questions: Have you travelled recently? Are you feeling sick? etc. then they had their temperature taken. Thankfully they had no fever, so they saw a Dr and a nurse, and my sister had a bunch of X-rays.
Not sure what happens if you're running a fever.
At least for some issues (broken bones) you can still see a Dr even in a busy place like NYC.