The battery terminal covers on new cars and car batteries are there to prevent short circuiting or arcing against the car body should something touch the car terminals so they are a good idea to keep the battery terminal covers on the battery.
However the battery cover terminals are not really necessary and won't cause any other problems with the battery or battery terminals.
And you can drive your vehicle without the battery terminal covers but I would recommend leaving the battery terminal covers on the battery though.
Because it prevents the battery terminals from possibly shorting out which could damage the vehicles electrical system as well as damage the cars battery or possibly start a fire due to the short circuit.