Pikachu yes, but as for Squirtle, Bulbasaur and Charmander, Professor Oak gives you a choice of one of them when you go to talk to him (can't recall if you need all 16 badges or the fight with Red done), and that's it.
There's also a guy in the Silph Co. building that gives you a choice of one of the three Ruby/Sapphire starters as well. (Again, think you need to beat Red for this, but it might just be all 16 badges.)
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