Yes biting your nails too often can cause damage to your teeth and should be avoided even though it can become a habit that is hard to break.
When you bite your nails with your teeth you risk damaging your teeth by causing the teeth enamel to splinter or for your teeth can break and crack.
Your teeth can also move out of place and cause crooked teeth when you get into the habit of biting your teeth and it's not hygienic either.