Can Pokémon acquired through the Global Trading Station corrupt your game?

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No, the hack Pokemon you hear about getting through GTS can not destroy your game.

These hack Pokemon simply have their abilities/stats modified. Such as giving them move sets that otherwise you can't get in-game or max EV/IV. The game won't be able to discern it from a regular Pokemon plus myriad of reasons why it just won't affect your game. It's just a Pokemon that has no malicious code behind it to do anything in your game. If you're into competitive battling, then it's best to stick to getting legit Pokemon to avoid any detection of using a hacked Pokemon even if it's legally hacked Pokemon (getting the moves/stats are possible in that regard).

Can hacked Pokémon that you receive through GTS or Wonder Trade corrupt your save file, or otherwise destroy your game? Is this something I need to be cautious about when I use the GTS?

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