Short answer is yes you probably could at the expense of losing a steering wheel function, either horn, cruise control or audio remote.

You need to route the signal through the clockspring because it is the only path that allows an electrical connection safely and securely no matter the angle and number of turns of the wheel.

A standard wire harness in that area would have to have enough slack to be twisted a couple of turns each direction and is gonna be thrown around numerous times a day.

Thinking about it some, maybe you can use some sort of mini radio transmitter to get the signal from the paddle to the console instead of the clockspring. Engineering such a system would probably cost you the same or more than just getting the heated wheel clockspring though.

A bit of searching showed some guys fabbing up remote shifters from car alarm transmitters and what not. Could be an option if you are a tinkerer.

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04 X5 3.0i auto
03 X5 4.6is