At our program, I know of Cards fellows/attendings who routinely scrub in on CABGs and transplants on patients who they've taken care of, the renal fellows on the transplant service are expected to scrub in on transplants, pulm fellows who scrub in on wedge resections and VATS and a few onc fellows who have scrubbed on a variety of tumor resections. It certainly happens and, if you have a good relationship w/ a particular surgeon, you're more likely to be able to scrub if you're so inclined.
Most IM subspecialists don't scrub in (or even observe) surgery on their patients simply b/c they're too busy to waste 8 hours in the OR when they essentially have nothing to offer other than another set of hands to retract the panus.