Depends on a lot of things, how its cared for, and the temperature and humidity playing important roles. Ideally you should add some moisture back into the leather at least once a year. If you live in a dry place, twice a year. The thing is to not overdo it, which can be as bad or worse than not treating the leather.
If you think about your own skin for a moment, you have a constant supply of water inside you, as well as moisture from bathing etc , and if a person uses lotions etc. your skin stays moist and soft. Leather is dead, no internal source of nourishment, so it only has a few directions it can go from there. Dry out and get brittle/crumbly (unless you add moisture back in), or rot from too much moisture, mold etc as well.
So to answer your question, no you don't HAVE to, a case can last at least 30 years from no oil as I have personally witnessed. But the leather is going to dry out as it ages, to the point that it will eventually fail. Could be a few years, could be 50 or 100. That part depends on the climate, how it was cared for etc etc etc. Think about old baseball gloves that don't get oiled. Your cases don't see that type of use, but the same thing applies.