I think it is. (edit: especially from the previous post)
White needs to have promoted a pawn onto a free black square, two of which at b8 and d8 will do.
Black can get all of his king side pieces out of the way, thanks to the g pawn being moved - including bringing the rook over. Getting the queen out of the way.
White plays his a pawn up to a5, rook escapes to b6.
Blacks a pawn takes rook, then white pawn in turn captures pawns on b6, c7 before capturing a rook on d8 (from h8 originally, can get to that square), promoting to bishop.
Black knight captures the bishop on c1 and the g pawn.
Yes, even with your stipulation of the king having not moved.
The g-pawn can promote by capturing three pieces (not pawns) and the f-pawn needs to capture another.
Queen and rook make two (the rook one of the last two captures - cannot escape from behind the pawns. Captures on f6/h6, g7 and either f8/h8.
Both blacks a and c pawns can promote. White moves his a-pawn forward to let out the rook, c-pawn takes rook on b, then a pawn. Both black pawns can promote to provide extra pieces (queen, knight or rook will do).