That's pretty close to Lyon's BoS, if they'd learn the Follower's advanced understanding of agriculture, medicine, and chemistry.
No, it's not, where did you get that from?
Lyon's BoS is willing to accept anyone into their ranks, as long as they can wield a gun and accept BoS law/rules, same as the Followers. This faction as I said, is not willing to just give tech and knowledge away, nor do they just accept people and let them be apart of the faction. They're selective, as I said, on who they give the tech and information to. They'd have a whole selective process they'd have created, that wastelanders would have to meet, to begin learning and advancing technologically and medically, etc.
They wouldn't be like the Lyon's BoS, West Coast BoS, or FotA. They might share some similarities as I said, but again, as I said, this faction would view the BoS (either West Coast or Lyon's), and FotA, as flawed since they lean to either one side or the other. One is too violent, the other too peaceful, while Lyon's BoS would be seen as too accepting.
If they were in the game, a character would need to have a high medical, science, and repair skill, along with a decent energy weapon or other weapon skill, to get much done with them at all. If not, they'd be very selective on what you were allowed to see, hear, and get from them. To join, would be difficult, and wouldn't just be a few fetch quests to get into their good graces.