Yes, you do. Shorter nails are better since it means your fingers will be able to grip a fingerboard better. If you can't grip, you can't press the strings enough and they won't sound good. They will sound muted and you won't get the smooth, flowing melodies everybody loves to hear. It’s like any other stringed instrument--your fingers are your most treasured asset and you need to keep them maintained.
If you don't want to cut your nails short (because the nail art on them is your pride and joy), you can still play! Don't worry about that much because it all depends on your fingering technique. It will take much more work to be used to this, though, so be prepared for that.