Is there any reason that you have decided against unlocking Birth Island in your LeafGreen game? Deoxys, like many of the Kanto and Johto Pokémon, can only be obtained in Ruby and Sapphire by trading with other games; its inclusion in the Hoenn Dex is misleading (if it were not included, it would only be found in the National Dex, with no clear affinity to any of the regions).
It is meant to be accessed from FireRed and LeafGreen, and as interesting fact, Birth Island is located between Six Island and Seven Island of Sevii Islands. It can, however, be accessed from Emerald - so there are no region traveling restrictions whatsoever (but technically, the Auroraticket had been distributed before Emerald was released in any of the countries).
I am not sure if you realize it, but there is a difference between downloading the Pokémon directly and receiving a special item which in turns triggers an event allowing you to obtain it in-game. Deoxys was recently distributed at the Houston Space Center as part of Journey Across America, in place of the Auroraticket. Does it matter? In so many ways, it does.
There are three potential problems that you need to consider:
Neither Mystery Events nor Mystery Gift have to do with transferring the Eon Ticket. But on the subject of Mystery Gift, it is unlocked in Emerald in the exact same way as in FireRed and LeafGreen.
This is the first time you've heard of Birth Island, isn't it?
