Yes an older gray can learn new words, tunes, whistles and commands. When I got my timneh 10 years ago, he was a passed around bird that had many previous owners. The vet figured he was already into his mid-20's, wild caught and imported to boot as evidence by his leg band.
This bird was not tame when I first got him, but after a year he trusted me and stepped up on my arm. He has learned to say many things that he hears me say and does so in my voice. He even laughs just like me. He is not a plucker or a chewer. He is never locked up in a cage and is free to fly about.
I just wish I could get more info on his age, but the vet told me it was impossible as the US government destroyed all animal Quarantine records back in 1990 or 1992. All he could tell me is that the letter code OUE means the bird was quarantines in California. My boy had certainly traveled more than me, as he now in New England with me, his forever buddy.
Per the vet he's in his mid-30's now which is considered old. He is healthy, eats well, gets feisty but he tends to nap more. He still says new things.