no, it can't.
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At the beginning, scroll down to mystery gift. It is the third option under new game. Click on that, and you should have the mystery gift that you are after.
as soon as you have obtained the mystery gift save game then go to mystery gift and you will get it straight away
You have to save your game and then turn you console off. Then turn your console back on and set up your Pokemon game. Before you start your game under 'New Game' its says mystery gift. You can only use the mystery gift if you have a connection cable for your gameboy.
I Generation 2 mystery gift is done with the infrared ports on top of the Game Boy Color. Mystery gift lets you trade mystery gifts with your friend.
You cannot get the same Mystery Gift item or Mystery Gift Pokémon twice per your current game save file however if you have additional games then you would be able to trade the related Pokémon that you acquired via Mystery Gift over to that other game and then you could delete the other one's game save file and then you could download another Mystery Gift Pokémon however downloading a Mystery Gift distribution is only possible while Nintendo has it active since its distributions are held for a limited time only.