In short no, if you wanna play a drake you gotta pay for privileged, and that means a pile of points. But I think your doing GM dis-service, lots of GM are open to discussion. It helps if you established history with GM, but many folks are open to cool game ideas, like an all Drake party, or all unique snow flake party. HMHVV varientes, some drakes, Pixies, maybe shapeshifters. GMs may be open to extra points or some other house rule to handle that sort situation, and if they aren't atleast you won't be as far behind.
Keep in mind karma gains aren't set in stone, and there are options like Cash to Karma. But yes it does take A LOT of karma to get a drake up, but when you do they are no kidding strong, adept or full mage, and you have really have a nut cruncher of a character. Now finding a GM who will run a campaign long enough to achieve that result is very difficult, but they do exist.