Short answer: Generally no. HMOs cover only in-network providers except for emergencies and pre-authorized referrals; routine out-of-network care is the member’s full responsibility.
Health Maintenance Organizations keep premiums low by limiting members to a defined network and coordinating care through a PCP. Outside of emergencies and care the plan specifically authorizes, non-network services typically aren’t covered at all, so the member pays the full bill. If you want out-of-network coverage, a PPO or POS plan is the better fit.