As Lordkat said, this usually depends on the coding and or the policy. If the policy allows transcare, it doesn't matter how it's coded; however, if they deny coverage for transgender care, then you need to make sure it is coded as something different like a hormonal imbalance. As for Callen-Lord, I was going to go there myself when I started my transition, but choose to go through an endocrinologist. The good thing about them, though, is that they have an in-house pharamacy, and I've heard they are lenient for those with low income.
In any event, I recommend you read up on your policy and see what you have. And to play it safe, ask the people to code it right, they are an lgbt clinic, so they will likely be okay with that.