Absolutely not.
For sixteen years, it's been Ash and Pikachu. I can't even think of a situation in which they would part, as there have been opportunities for them to do so, but they obviously never have. The only situation I can come up with is if Pikachu died, which I doubt they would do in a children's show. It would be very difficult for the show to transition Pikachu out, and transition a new pokemon in, no matter the circumstances. What would they even replace him with? It wouldn't make much sense to say "Pikachu is gone, now Ash has a cubchoo" or whatever pokemon they replaced him with.
Beyond the show, Pikachu is the mascot of the entire franchise, and replacing him is a decision that no one involved with the running of the company would ever make.
I agree, the show has changed a lot over the years, but that's all the reason to keep Pikachu with Ash. That team is the thread that ties all of the seasons and episodes together, no matter what changes happen in the show.