Yes, he's doing what you think he's doing.
Graham is a climber.
He DOES prefer the cat tree, but he will travel up the curtains as well.
Check out that gorgeous set of markings on his back.
(Oh how I wish my feet weren't in the reflection!)
He travels all the way up to the curtain rod.
But there's no reason to worry about him...
He comes down the exact same way.