I applaud Susan's for enforcing fair discourse about this topic. I am a member elsewhere and am very disappointed right now at the behavior on that site.
As for federal courts, they have jurisdiction over the military in any matter related to human rights, constitutional questions, etc. Is someone here suggesting that the Supreme Court cannot force the military courts to accept a SCOTUS decision? The military has often reacted in direct response to a SCOTUS decision. In fact, the recent SCOTUS decision striking down DOMA resulted in the military beginning to pay spousal benefits to service members who are legally wed to their partner.
TL;DR: the short answer is yes, if a federal court rules that denial of HRT and transitioning is "cruel and unusual", then the military justice system has to abide by this.
I think the ACLU is fully qualified to know this, else why would they be threatening to sue in federal courts? Those folks are lawyers and know exactly where to file such a case.