Good god, do not do that when you're on surgery. They're called core rotations for a reason, and your surgical residents and attendings will likely notice if you're spending most of your time on the wrong side of the curtain. Beyond just the optics, learning about surgical procedures and the medical care of surgical patients is important for the practice of anesthesia- the best anesthesiologists are acutely aware of the steps/progress of a particular procedure and are ready for any contingencies which may arise. Spend your time on surgery learning about surgery.
As for how to get exposure, most schools are moving towards allowing some elective time during third-year. If your school isn't one of them, you may be SOL.