Since the power is
Shift (Dracoform), and the Shift power is defined as a Critter power (
Runner's Companion, p. 85), I'd say it's possible. And since that same definition says that the creature gains "all non-paranormal abilities innate to that race", then you'd gain the Hardened Armor, Flight, Senses, etc.; but not Dual-natured, Elemental Attack or Mystic Armor powers.
Also, you only gain the power for (Magic + Initiate) Combat Turns. Unless you spend 3 Karma immediately, then it lasts for (M+I) days. So, you'd need a large Karma reserve to use this more than once or twice on a Drake. And when you run of of Karma...