I'm simultaneously hunting for a Shiny male Burmy in HeartGold and SoulSilver (via Special Headbutt Tree). I would try to SR it in DPPt instead, but I'm really wanting to get it in a Friend Ball!
You can, but you have to transfer them to B2W2 first (the original BW isn't compatible with Poké Transporter). You can even send Pokémon from Gen. III to the newer games if you have a DS Phat/Lite to migrate Pokémon via Pal Park in DPPt/HGSS.
However, if I recall correctly, Pokémon obtained prior to Gen. 6 aren't allowed in official tournaments.