I imagine the answer would depend on the doctor who would be prescribing your hormones. I don't think mine did. That you have a referral is one thing, but if it's old, who knows what's happened in that time? Who knows if you are still on the stable footing that the therapist thought you were when they referred you? That would be my point of view if I were a healthcare provider, but I'm sure there are others out there who would accept the referral at face value.
I agree with invisiblemonsters. I'd wait a bit and save up. Make a separate bank account for HRT related expenses, and once you have half the money you would need, go ahead and start with therapy. Mostly for the reasons mentioned above, but also to prevent you from ending up with therapy that drags on longer because they know you can't afford to move forward (I would hope a therapist wouldn't do that to you, but you never know).