Yes, your expenses are tax deductible. What do they qualify under? That's a good question. As a military pilot, you would likely be able to claim it under the lifetime learning credit, but that is income dependent. However, you may have a hard time claiming it under any other clause. An ATP is not required to be a pilot in the military. You might be able to justify it under the clause of maintaining or improving skills in the same field of work.
For me, it was a no brainer. My company flies jets and light turboprops. Without an ATP, I would never be eligible to fly the jet as a captain. That would be the express requirements of my employer. When I had my CFI in a helicopter, deducting my expenses to become a CFI in airplanes was valid because I was improving my skills in the same field.
Will it attract attention? Maybe. I feel confident in the defense of my tax return, so do the same if you feel the same confidence.