I mean, he's one of like 4 neurosurgeons that people go see, right? So you could be traveling from all over
My experience with the US health insurance system (currently) is that a) either it's being offered to you via an employer, in which case you won't have a lot of choice with the plan you get, or b) you're purchasing it on the ACA-mandated "exchange", or c) you meet qualifications for Medicaid or Medicare.
I believe that out of network benefits would only really apply for (b), when you have a choice of which plan to purchase. There are usually various tiers of benefits available to you based on the insurers in your area. Some of these will have out of network benefits and others will not. This should all be pretty transparent on the exchange website (either Healthcare.gov or the equivalent version for your state.)
Unfortunately, in my experience even with the highest-tiered plans, there is usually a sizable deductible before out of network benefits are covered. And even then, I imagine that most insurance companies have ways of fighting your claim, depending on what they deem is "medically necessary".
Apologies if this is basic info that you already know. Maybe someone can chime in with state-specific info, or even better, maybe there is another patient of the same doctor who has had success with insurance coverage for their treatment.