Short answer: Only in limited cases, and only if you agree in writing ahead of time. An out-of-network provider can balance-bill you for some non-emergency services only after giving you advance written notice of the estimated cost and getting your signed consent. You never have to sign, and consent is barred for emergency care and key ancillary services.
The No Surprises Act protections can be waived only through a specific notice-and-consent process. The provider must give you a written notice (on paper or, if you prefer, electronically) explaining that they are out-of-network, an estimate of the charges, and that you are free to seek care from an in-network provider instead.
You must knowingly sign that consent before the care; a provider cannot spring it on you or bury it in paperwork. Consent is never permitted for emergency services or for certain providers you cannot realistically choose, such as anesthesiologists, radiologists, and pathologists at an in-network facility. If you do not consent, your surprise-billing protections stay in place.