Yes. A flat battery means your car’s alternator has to work harder to recover the battery. This puts extra pressure on the engine and uses more fuel.
Always keep your battery charged and replace it as soon as possible if it’s going flat.
Disclaimer: Every car battery is different. Without actually examining the car, it can be hard to figure out exactly what’s actually going on with the battery. If you’re having trouble with yours, you’ll get the best advice from a professional. And always get it looked at as soon as possible, so that small problems don’t get the chance to grow into bigger ones. Never drive your car unless you’re certain it’s safe to do so.