Sometimes. It depends why the first surgeon would be unable to do the procedure. If the problem is that the patient might not wake up from anesthesia because of problems with heart disease, lung problems, or other metabolic issues, then it doesn't really matter what the surgeon has to say about actually doing the procedure because the anesthesiologist is the one saying "no". If it's an issue of too much adipose, sometimes it would mean that the surgery would take longer than it's safe for the patient to be under anesthesia.

Another possibility is that the first surgeon operates at a facility that doesn't have access to more advanced technologies or other medical specialists in the event that something goes wrong. And there are some surgeons that are just more willing to accept the risk of a bad outcome, and I would argue that that's rarely in the patient's best interest. There are alternative options that the surgeon should discuss with the patient as part of the informed consent process, and sometimes, the alternatives to surgery are just safer than the risk of the surgery itself, even if they aren't as effective or are a long term treatment (ongoing) as opposed to a definitive treatment (cure). If the patient has a high risk of serious complications, up to and including death, then attempting the curative procedure might be more risk than it's worth compared to a long term medication that mitigates the disease.

You'll see this with pregnant patients too. For elective procedures that have safer alternatives or temporizing measures (a holdover treatment until surgery is safe), those are generally preferred to putting a pregnant patient under anesthesia because of all the cardiovascular, immunologic, and other physiologic changes that happen during pregnancy alongside potential risks to the fetus.