I have a question, I see a lot of people asking for Celebi's and Darkrai's etc. I'm wondering can you actually trade them? I know you can't deposit them in the GTS as the game stops you, so if someone had a shiny Giratina and asked for a Celebi for it, would someone even be able to trade their Celebi for it or not?
No. The trade wouldn't go through.
As to why people do it, I'm not quite sure myself. They could do it because of two reasons:
So a basic summary is No. This is because the GTS in Gen 6 is programmed to not allow any Mythical Pokémon(Secret Legendaries that are obtainable only through Events)through. Mythical Pokémon are hard to come by and thus, keep them for safe keeping. Game Freak realized that people who get Myhticals, tend to trade them for common Pokémon like they're stupid, so that disabled the trade of Mythicals. So now, people on GTS are teasing you since you can't trade Mythicals.