No, they are too busy working.
However, in the academic setting there have been some hybrid operating room/cath labs created. I.e. patient can get a stent put in, and then a bypass, etc. This keeps patient from having to have procedures at 2 different times. So in those cases both surgery and cath lab cardiologist might be in there at the same time...but usually not the WHOLE time each is working.
They do sometimes have joint conferences to discuss difficult/complex patients, at least in academia. For example, cardiologist might ask, "Are you willing to do a valve replacement in this difficult patient". Surgery folks might argue back/discuss, wanting details of how bad is his lung disease, how bad the heart function now, etc. This helps them decide if it's too dangerous to operate, will it likely benefit the patient, etc.