I doubt they have a Adventurer's Guild but I could see them having a government department that handed out licences and contracts to freelance soldiers and explorers. The strength of the Adventurer's Guild over traditional military in Eorzea is the diversity of the skillsets of it's members allowing adventurers to solve many issues that are awkward for a traditional military's rigid structure to solve efficiently. The Garleans would see the advantage of having multiskilled freelancers solving problems that would be inefficient to mobilise Garlean might to solve. It would be however strictly overseen I suspect.