Absolutely, any hospital will treat you regardless of whether you have insurance. Insurance plans can't make you pay more in co-payments or coinsurance if you get emergency care from an out-of-network hospital. They also can't require you to get prior approval before getting emergency room services from a provider or hospital outside your plan's network.
What you pay out-of-pocket for your emergency room visit depends on the plan that you choose and the hospital you go to. This care may be subject to a deductible, for example, or a hospital may have particular cost-sharing rules in place.