It is possible to get Double agent with a DK being your second character. You can also send anything that is Bind to Battle.net account across faction as long as they are on the same server.
Dont know how it works now, but at the start of MoP you would even get Double Agent if you faction changed your lvl 90 character.
I faction changed mine from Alliance to Horde 4 days into MoP and got credit for the achivement when i logged onto Horde.