Nope. Most military flight surgeons offices (at least in the USAF) can and will give you a simultaneous FAA Class 3, but unless they actually sent their techs and docs off for a little FAA training, they weren’t allowed to do higher classes of FAA physicals. At least not when I was in. At one point in the distant past they apparently had had carte blanche, but a number of offices were apparently sloppy about the paperwork and that gentleman’s agreement went away.