AI's typically have bodies that come with them but from what I understand of Halo/RvB they only show up as projections and lack a real body (a la GLaDOS) . Correct me if I am wrong here, since my answer is based off this assumption.

Generally, the essence of the character would be what the dragon mages save, since Azeroth in the primordial era lacks any sort of technology to install a chip in. With that in mind, being that their soul is detached from their body, they would arrive as undead spirits in the image of the player's choosing.

If further elaboration is needed, feel free to ask.