Call Mesa to find out if it is approved for VA Benefits. Either way, you will have to take out a loan for something. As you can't rape the VA benefits by using you GI Bill for BOTH flight training and college costs (as far as I know. . . I could be wrong, but everyone I have spoken to has told me it can't be done, one or the other only.)
You can use the VA benefits for Part 141 flight training above PPL, or you can use your GI Bill for your tuition and school costs, etc, and take out a loan for the flight training.
Good luck.