Yes, a 12-volt dc battery can be used to power your led neon. whether it's lead-acid, lithium. a 7Ahr Battery could comfortably power a small neon sign for a couple 4 hours.
Batteries like this range in price from as low as $40 for a lead-acid type and $240 or more for lithium. You will also need a battery charging unit to recharge the battery.
Depending on the batteries capacity and the size of the neon your runtime will change. Larger signs will require a bigger battery something similar in size to a car battery.
In the case where you want the battery to last for several hours, it would be worthwhile to invest in a bigger battery. If weight is an issue then two battery units so could be the right choice. with two batteries you can easily swap them when one needs a charge. This way you could keep the same sign running for a much longer period with minimal downtime.
No, you won't need a led driver when the sign Is powered by a dc battery. the sign won't need to be run through a transformer because the power from the battery is already 12v DC (direct current)
Our neon lights have to be plugged into a power socket.