I'm pretty sure they do actually let you do this. A few years back I preordered a game from their website and it didn't turn up on release day, I went to my local GAME and explained the situation and they sold me another copy, and told me I could come back and get a full refund with the sealed game that was still in the delivery process. I did, and it worked fine. Took a few days for the refund to come through.
Thanks for replying - that sounds very reassuring!
I also wonder if they can actually tell the difference between the two copies though, unless each of them has a unique barcode or something. I can't see the barcode of my current copy anywhere on the receipt either.
Edit: to finish my story, for those curious: my plan did work and my mailed copy has now been returned to the store in place of the copy I bought there earlier to be able to start playing on Friday. As long as both are sealed, stores like GAME can't tell the difference. Handy to know in future situations like these where an online ordered copy is being delayed while the game is readily available in physical stores.