Yikes. I sure wouldn't risk flying without a health certificate. I have been asked once for mine, at security, not the check in counter. They were very nice about it, just asked to see it when I had to show my boarding pass and ID.
It is the Department of Food and Agriculture that regulates this.
I can't even imagine being turned away because I didn't get one. That would be awful and I doubt you would get a ticket refund!!