Save states? Recent games lists? That's not what the SRAM is used for! The SRAM is used by games that has extra RAM (specifically a "Static RAM" chip or SRAM for short) in the cartridge. Just starting a game that's using SRAM may be enough for it to be accessed. You can't choose not to use it. Technically a game can include a SRAM chip without battery, just for the sake of the extra work RAM without the ability to save. I don't know if this is common on the GBA though. It is common on NES and Gameboy since those systems only has 2kB and 4kB internal RAM respectively.
I don't know if you can have SRAM in addition to EEPROM or FLASH in a GBA cartridge either.
Besides, accessing the SRAM has no significant effect on the battery life. The battery is always discharging no matter what you do.