As far as I can calculate, 6 is the limit for the most number of pawns on a single file possible. Is 7 possible at all, ignoring promotion? I only took into account using the edge of the board, not the center, so I may be wrong.
Using black pawns, many thanks to @DM for this idea, I have completed my quest to find the perfect 7-pawn-file proof game. I used black to shave off half a move.
[FEN ""] 1. d4 b6 2. d5 a5 3. d6 exd6 4. Qd5 c6 5. e4 cxd5 6. b4 f5 7. Bd3 fxe4 8. c4 exd3 9. c5 bxc5 10. Be3 axb4 11. Nc3 bxc3 12. Bd4 cxd4 13. O-O-O g5 14. f4 gxf4 15. Rd2 cxd2+ 16. Kb1 f3 17. Ne2 fxe2 18. Rd1 exd1