Many of our guitars come with a battery, but not all are necessarily "active".
The only guitasr we make with active pickups are the Luke and BFR Luke, which are made to Steve Lukather's exact specifications including the EMG pickups.
The Luke 3, JP13, JP15 and Majesty all have active preamps with gain boosts that are powered by a battery.
Game Changers all have circuits that are powered by a battery.
The Albert Lee and Silhouette Special are equipped with the Silent Circuit™, which will allow single-coil pickups to be heard without the 60 cycle hum. The batteries in those guitars power that silent circuit but the guitars will function without a battery.
Petrucci guitars with the piezo option require a battery to power the piezo.