Yes, an electric cooler can definitely drain your battery if you leave it plugged in when you’re not driving. However, quality electric coolers have built-in battery monitoring and will shut down before draining your battery beyond its ability to start your car.
Depending on the power draw, cooler size, and temperature, it could drain a car battery in a couple of hours to a couple of days. And at that point, the cooler will turn off, possibly ruining your food.
Therefore, you should plan to keep your cooler plugged into the car while driving. But when stopped, it’s wise to have a secondary power source in case your car battery runs low.
A large battery bank or solar panel and battery pack (we love the system from Generark!) is a good way to get extra energy to your cooler.