As the Battalion Education Officer, I can help you out. Here's the key bullet from MARADMIN 571/05 (Don't know what service you are):
E. TA FUNDS ARE AUTHORIZED FOR VOCATIONAL AND TECHNICAL,
UNDERGRADUATE, GRADUATE, INDEPENDENT STUDY, AND DISTANCE LEARNING
PROGRAMS. COURSES MUST BE OFFERED BY INSTITUTIONS ACCREDITED BY
AGENCIES RECOGNIZED BY THE UNITED STATES DEPARTMENT OF EDUCATION.
So the answer is yes and no. Yes they will fund it (it's considered Vocational), but only if it's at an accredited institution. So, the local flight school doesn't qualify but some place like Embry Riddle would.