Well I guess they could still be around, and I have seen posts of people that expect the Empire to still be around even though they lost a lot of Yeerks to nothlitism, Earth, Leera, and the Anati system in the timespan of three years.
Of course they still have the HB Homeworld, assuming the resistance fails. They sill have the Taxxon Homeworld.
I probably shouldn't just assume the Empire fell apart within the next decade after Earth was won, but another 300 years? That's a stretch.