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It should be noted that although, as you say, a generated Pawn will block one element of a double check, there are some circumstances where the Pawnb itself will check. If a White Knight moves from c7 to a6 and the Black King is on b8, both Knight and Pawn will give check. If there is a Bishop or Queen beyond the Pawn (say on e5), that will protect the Pawn.
I do like this idea. However, here is one possible subvariant: A pawn can promote to a queen if you have no queen (so you cannot have two queens). A pawn dropped on the last row still won't be a queen, though. (The game is probably good whether or not you use this subvariant)
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