Is it possible that wearing a dental night guard for night grinding affect my bite?

Depends: If appliance is flat plane, it will allow your muscles to go to tonus position and this is where your bite will fit best. You may need an occlusal equilibration to make the teeth fit together at this relaxed position.

Absolutely: The night guard needs to be periodically evaluated by your dentist. An ill fitting appliance will cause more harm than good.

Yes: Your bite changes throughout your life. Just as you have increased attrition, your vertical dimension, your bite/occlusion will change. Wearing a guard can be also problematic if you have torque, interferences, premature contacts, etc.... Be involved with your dentist on your guard, orthotic, or appliances.

Possibly yes: Make sure your bite on it is even.