Short answer: Yes. Once the deductible is met, an HDHP can apply copays or coinsurance. Before the deductible, an HSA-qualified HDHP can’t use copays for non-preventive care; except ACA preventive services, which are always covered at $0.
On a high-deductible health plan, cost-sharing works in two phases. Before the deductible, an HSA-qualified HDHP generally can’t apply copays to non-preventive services; you pay the negotiated rate, though ACA preventive care is always free. After the deductible is satisfied, the plan can charge copays or coinsurance like any other plan. (Plans can also cover certain ‘preventive for chronic conditions’ drugs pre-deductible without losing HSA eligibility.)