Well, In terms of the Great Intelligence mentioning that the Valeyard is known in the future, it is well shown that the Doctor will use that name pretty freely. He has listed it among his names and achievements many times when trying to establish that he is not be messed with so I don’t find it a far stretch for some Doctor of the future to either use the name as an alias or mention himself as the Valeyard in a well documented moment like a history changing speech. I just think that the Doctor comfort in owning up to that identity as his own makes what the Great Intelligence said strong suggestion of the Valeyard future existence but not proof.
PS. The master refers to the Valeyard as “An an amalgamation of the Doctor's darker sides from between HIS twelfth and final incarnations". This could be refering to the future form of the current Doctor in the room(6) and his gender currently. Or it could be a hint as to which Doctor he and the Valeyard identify as the 13th. 674
My personal belief is that sometime in the future, something happens that causes the Valeyard to sever from the Doctor and take a physical form but without his memories. This Doctor would then find out about his other form and check up on his mishaps such as when the old man in the gallery above the UNIT vault met with the 11th Doctor and suggested that he was a future Doctor. Then, this anti Doctor would end up discovering all the things that caused him to become the sentient voice in the back of the Doctors head that wanted to break free. This would cause him to turn into the <PERSON> we see in the show who is intent on destroying the Doctor and becoming powerful. I like the idea that the Master found <PERSON> and tricked him into Becoming the <PERSON>. Then once an opportunity presented itself, he allowed the Valeyard to become known the the High Counsel of <PERSON> and for the events of the 6th Doctor’s trial to take place. 837