Will constant use of in-car charger damage battery?

This will depend on what type of car charger you have. If you have what is known as an "intelligent" charger it will cut the charge rate from full charge down to trickle charge when the battery is full. 

On the other hand if your car charger is not this type, it will charge the battery continuously at full charge rate and this is when your battery suffers damage from overcharging and its performance and efficiency will be effected. 

An easy way to check what type of car charger you have is to feel your battery after it has been on the car charger for about 2 hours. If the battery is hot it is likely that you do not have an "intelligent" charger.