Y'know, during the Johto League, Ash had Pikachu with him while also using six Pokemon against Gary (which contradicts when he caught Krabby...). I wonder if it's possible for him to have Pika following him without being "officially" in the party.
...Yeah, not gonna happen, just a "what if" thought.
I'm pretty sure Oak came there and said something about bringing with him Ash's Poké so he probably had access to all of his Poké, but only 6 of them was officially "with him" while some were considered "with Oak" but Oak brought them there for Ash
So no, Ash can't have more than 6 and Pika does count