Can Brynhir stop Aurora's revealed unit from being played after Thrill of the Hunt?

Yes. Aurora's trigger stays on the chain. If you respond with Thrill of the Hunt and replay Brynhir, Brynhir's effect resolves first and stops your opponent from playing cards this turn. When Aurora later resolves, the revealed unit cannot be played and remains banished. If you let Aurora resolve first to see the card, it is too late.