Advantest test equipment does not store calibration data in battery-backed ram, they use eeproms. The battery powered memory only stores configuration information, so it retains its setup across power cycles (like the old days when equipment had mechanical switches). This is true for every piece of Japanese test equipment I own, not just Advantest. Without the battery, you'll have to go through all the settings each time you power cycle it, but apart from the inconvenience there is no loss of functionality. However, replace the battery immediately, and clean the area around it carefully. The battery will reduce the unit to scrap if allowed to leak.
I don't know about this particular Advantest model, but in general with Advantest equipment one issue you can run into if the battery fails is that if the ram does not contain a valid set of configuration parameters (which it won't) the unit can crash during its boot sequence instead of recognizing the problem and resetting to defaults. If you search around the internet you can find a document of Advantest reset sequences, i.e., combinations of buttons to hold down during power up to reset the configuration ram. I needed to do this for an R8430 after replacing its battery.