So this is a fair question... but one that has zero bearing on hours of experience.
Now I'm not a surgeon, but I'm going to guess the answer to that question is "no." for a variety of reasons.
1. The same issue with any combined multispecialty training. For example, the anesthesiologists who dream of doing cases one day and ICU the next day or EM-CCM who wants to be in the ED one day and ICU the next day. If I'm scheduling people for the ICU and you're full time, then while I might want to accommodate a schedule request, I might not have the ability to do so. What happens if you're scheduled to both cover the ICU and run cases at the same time? It's not like you can up and leave to go to the bedside of a crashing ICU patient.
Now, sure, a surgeon can't up and leave the case either, but that's what normally their midlevel is doing while they're in the case as well as the ICU team.
2. The surgeon doesn't command the anesthesiologist. So what happens when what the surgeon wants to happen in the SICU conflicts with what the anesthesiologist wants to do in the OR?
3. Knowledge is a factor. There's only so much people can retain and when it comes to being an expert in a field, it can be hard to keep up with multiple fields at the same time. The ICU is not the OR and the OR is not the ICU, regardless of the skill set and knowledge set overlap. One of my biggest complaints regarding midlevels, especially NPs, is the non-sensical aspect of how they can jump from specialty to specialty. I know one NP that will cover for hospitalist shifts one day, ICU shifts a second, and ED shifts the third. Heck, the entire concept of acute care NP is pretty nonsensical as the aspects of treating inpatients, emergency patients, and critical care patients are all distinct things.... which is why EM doesn't do inpatient, IM doesn't (for the most part, and when they do it's often done poorly) EM, and for both to do critical care well, it's additional years of training.