Highly, highly, HIGHLY unlikely.
First off, who would just throw a shiny legendary on the GTS? That’s crazy. They’re insanely valuable. Second of all, the GTS, ESPECIALLY in ORAS, is flooded with hacked Pokémon, almost always shiny. They request impossible things, like extremely low leveled legendaries (to the point where it’s not possible to obtain them) or Magnemites with a certain gender. There’s often a lot from one hacker-you might see 10 shiny Dialgas from one hacker. It’s not impossible to put a shiny legendary up on the GTS, but they’re too rare and valuable, and there’s a huge amount of hacked ones out there, so it’s EXTREMELY unlikely. You’d probably be better of shiny hunting the legendary, that quite literally has BETTER odds than trading for shiny legends on the GTS (which you usually can’t anyway due to the impossible requests).