Yes, the "resistor" (It is really a PWM regulator) is powered by battery supply and has it's own ground. A defective 'resistor' (Damn, I hate called it that) can sink a bit of current and can even run the fan motor without being commanded to.

If you have doubts about it, just change it. They are cheap ($30 or so with shipping) and are a known failure item in these cars and numerous Mercedes products.

Search "Mercedes SLK320 Blower Motor Resistor" (prices range from $23 to over $400 for the same damn part). They plug in and I believe you need a #1 or 2 phillips and an 8mm socket to get to them.
It helps if you are in really good shape, cause they are accessed from under the dash.