Is it possible - or impossible?


Impossible. White's pawns must originate from a- to f-files (they made at most 9 captures; those from a- to f-files make precisely 9 captures to reach that stack, and g- and h-pawns will take more). Similarly, Black's pawns must be c- to h-pawns. All captures are to stack the pawns. But then Black's a-pawn cannot be captured by White.