Is this possible?

It probably is.
I don't know why you'd want to, but I'll be surprised if nobody has done a bit of X1 drifting before.
 
If you count this drifting, but my opinion is that isn't drifting....

Since that is how it handles...
 
I say no, it's not possible. As JK83 mentioned, the car handles a very, very unique way. It isn't heavy enough to slide around, and holding down the handbrake for only a few seconds will make you spin out into a wall.
 
Actually, now that I think about it, I have the lovely, sub-400hp, fan-disabled 5G version... I wonder if I can drift that?
 
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