YES. That's exactly what happened. I haven't seen that episode (actually, sadly never watched much of ER. I was more of a Chicago Hope girl) but, yes. And that... would be very much of a holy shit moment.

The conversation at home went like this:
Me: That's... the drug I'm on.
Dad: If you had Pneumonia, the doctor would have told you.
Me: *goes into coughing fit*
Patient on House: *goes into similar sounding coughing fit*
Me: You... uh, were saying?

... yeah. Freaky when that happens.