In theory, yes. Still, I have yet to see any Ishgardian soldiers who aren't martial weapon wielders; they're all dragoons or lancers or something.

AST is implied to be a job that takes a lot of training to use the magicks it's capable of. If it doesn't provide an immediate benefit to the war effort (and, like every class, we're prodigy ASTs), Ishgardians don't care.