I think my case has similarities with yours: I have class 2 jaws but had orthodontic 'camouflage' treatment previously so my bite was almost class 1 with no crowding when I started consulting with surgeons. I was told that surgery first was an option in principle but I would end up with an underbite which, according to the surgeon I spoke to, would look so bad that he refused to even offer me that option even though it could have been fixed with braces afterwards. Another surgeon also said surgery first was an option and he would remove lower premolars during the surgery, which would increase the risk (and the cost) of the surgery significantly (more cuts, less accuracy). So I opted for lower premolar extractions and braces to close the gaps prior to surgery.
I was also told that it would take 6 months but in hindsight I don't think that's realistic, it is more likely to take at least 8 months or so to close the gaps. I have a really good orthodontist that I see every 3 weeks (!) to get my braces tightened and he also uses powerchains and I wear elastics and the braces are self-ligating etc. and it will still take around 8 months to have a large enough overbite to perform the operation (and the extraction space will probably only be fully closed afterwards). Obviously wearing braces isn't fun and now the gaps are closing I definitely look worse than before because the overbite is more noticeable, but hopefully this is only for the next few months and then things will improve after the surgery.
So to answer your original question: I would not trust a surgeon that told you it is a good idea to perform surgery first if it will mean you will have an underbite after surgery and tried to downplay it like that's not a big deal.