No, these systems do not consume energy when activated. While there are several different designs, all are based on a motorized actuator that engages the brake. So it only is "on" for the short time it takes to push the brake shoes or pads into position. Then it's on again for the time it takes to move them away.
Basically, no ... it's no different than parking on a side slope. Even in your case it sounds as if the "side slope" really isn't that much of a deal. Just like parking on uneven terrain ... and ... yup, that's exactly what's going on. :o) Shouldn't be an issue at all.