True, if the airline requires it. Delta and United do not require it and will accept your app without an ATP. US Airways doesn't require it and the last time American hired they didn't require it either. One of our guys asked their recruiter if he should just go get it and the captain looked at him like he was an idiot. He said we give it to you in training (STS), so unless you have a couple grand burning a hole in your pocket, I wouldn't waste your money. He still got interviewed and hired. But yes, I know FedEx/SWA require it and it never hurts to check the container, but it's not necessarily a requirement.
You will only need to have an ATP to fly pax. So unless they are proposing a rule that says you have to have an ATP to be hired, you should be ok. Most airlines will give you your ATP as part of your check ride in training (that's how I got mine). But all the ones I have seen recently just say you need to have ATP mins.
I'm only pointing this out because if they don't give the mil an exception, this could cost a lot of $$$$. Being military, I can't see that not having your ATP will hurt you too much, especially if they truly need as many pilots as predicted. Now if you really want SWA/FedEx then you're pretty much screwed into paying the money.