@hi_cial gba games, except for a *very* few early ones like Fire Emblem, use non-volatile flash memory for save data! So they don't need a battery any more than your usb flash drive needs a battery
except pokemon rse, which have a battery for timekeeping because they also have a real time clock (but if it dies they don't lose the save, time-based things like berries growing and espeon/umbreon evolutions just don't happen)
-F