Great question! No, an electric vehicle does not pollute more than a gas vehicle. Even though manufacturing the battery for electric cars does require a lot of energy, over the lifetime of the electric vehicle, it pollutes less than a gas vehicle.
There are two main parts to this question: the manufacturing process and emissions over the life of a vehicle. The manufacturing process of creating the electric vehicle battery is when the highest level of pollution associated with EVs occurs.
However, the lifetime of the vehicle is where the EV makes up for the battery footprint. Because EVs have zero tailpipe emissions and produce fewer greenhouse gases during building, they can go their entire lifespan without creating half the carbon footprint a gas-powered car will.