Short answer: Possibly, yes. The rule that preventive services are covered at no cost generally applies only to in-network providers. If your plan has a network and you get preventive care out-of-network, the plan can charge you cost-sharing, or may not cover it at no cost at all.
Federal rules require most health plans to cover a set of recommended preventive services, like screenings, immunizations, and well visits, with no copay, coinsurance, or deductible. But that no-cost guarantee is tied to using an in-network provider: these services are covered at no cost to you when provided by an in-network medical provider.
A plan that has a provider network is not required to provide those preventive benefits at no cost when they are delivered by an out-of-network provider. So before a preventive visit, confirm that the provider, and any lab or facility involved, is in your plan’s network, or you could face a bill.