Nope.then she would be the first sidekick character with more than 3 Pokemon on hand, would she not?
Misty had Staryu, Starmie, Goldeen, Horsea, Psyduck, and Togepi at one time. Then when she left Starmie and Horsea at the Gym she caught Poliwag so she still had more then four.
Brock had Geodude, Onix, Zubat, and Vulpix at one time. I think Pineco came after Vulpix was gone.