I’ve been told that class dates are several months out and it is best to apply a few months before you hit the Ratp minimums.

One of the questions on airlineapps asks “Are you currently eligible for an ATP or a Restricted ATP”

I would imagine checking “no” means your application is automatically tossed out, right?

Anyone check the No box and still get an
interview?

Depends on the airline. I bet regionals will lead your ATP eligibility, I know jobs and class dates have been granted based on people's expected timeline to R-ATP mins.

Doesn't hurt to submit an app and be honest about it. You might called early, or you might get credit for "app longevity" down the road.