Yes Professor Oak most definitely remembers meeting Ash as a boy. If you listen real closely at the end of the film Professor Oak is flicking through his sketch book (you know the sketch book that he used to sketch Pokémon as a boy) and says:
"Hmm it seems like it happened only yesterday".
Because he still has the sketch book to this day and because of his smile you can tell the sketch book and memories of meeting Ash and Celebi are sentimental to him. He also sketched Ash's Pikachu and Celebi together sleeping when he was a boy.
This is a picture of Pikachu and Celebi that Professor Oak sketched as a boy:
This is the same picture of Pikachu and Celebi when Professor Oak opens his old sketch book at the end of the film:
Notice how time has left it's mark on the sketch book with the sketch of Pikachu and Celebi being slightly dim and faded. After looking at the sketch Professor Oak simply smiles and says "Hmm it seems like it happened only yesterday".
Source: Pokémon 4Ever - Celebi Voice of the Forest Movie
Hope I helped :)