No. Because the PPL is initial training for career, it's not deductible. Check with your accountant for correct IRS citation. However, if you are already in the aviation industry as a pilot, then additional training, such as an additional ATP, may (and I repeat MAY) be deductible.
Example - professionally, I'm both an engineer and university faculty. I can deduct books, software, hardware, even my DSL line at home because they are direct expenses (work and teaching), and advancing my technical knowledge. I cannot deduct mileage to/from work or the university.
But I cannot deduct the costs of courses I take in departments outside mine at the university because that's not my line of business. On the other hand, I don't pay tuition for those courses, either.