It is highly unlikely. Pikachu has shown that he personally does not want to evolve into a Raichu, despite that meaning he will gain higher stats. Ash has respected that as his trainer, and has helped stopped Pikachu evolving many times.
There have been times when Pikachu has considered evolving, but has ultimately wanted to stay the same, since once he evolves, he can't turn back.
Besides, not all of Ash's Pokemon evolve; Gible, Squirtle, Bulbasuar to name a few.
EDIT: Also, the anime doesn't stress evolution as the only way for a Pokemon to gain more power; it's not the be all and end all for a Pokemon, as it is in the games (esp. with competitive battling).
I just found the episode I was thinking of:
It was one of the few episodes that I actually remembered.