The Latent Dracomorphosis quality (see Howling Shadows, p.164) grants you a Magic attribute of 1 unless you already have a Magic attribute. We can infer the same condition for the Drake quality (HS p.163) -- i.e., if you don't have a Magic attribute, this quality gives you the minimum 1 point. If you already have a Magic attribute from priority allocation, use that one instead.
When you take the Drake quality at character generation, you start with all the basic powers of a drake (including the magic attribute), but those powers are mostly limited to the drake form and you can't use the Shift (Dracoform) power until you finish paying off the Karma debt. So you have them, but you can't use them right away. The Karma debt left over from character generation isn't doubled, but it has to be paid before you can spend Karma on anything else -- i.e., every point of Karma you earn goes straight into the debt until it's paid off.
Talk to your GM about this ... he might agree that it's no fun playing a Drake character who can't use his powers for the first few shadowruns (which could be months of real time). The GM could grant a starting Karma bonus to everyone in the group, sufficient to cover your drake debt. That way, you start with a full drake and the other players can advance their characters a bit before the campaign begins.
