Warrant officers formed the sailing navy's technical middle tier

Did the Royal Navy have an NCO corps in this period?

Yes. Masters, senior carpenters, and other specialists held writs or warrants rather than commissions, forming the professional tier from which the warrant-officer tradition developed.

The early Royal Navy included officers whose authority came from writs and, later, warrants. Sailing masters and senior carpenters were among these specialists. Their warrants came from the Admiralty or Navy Board, while commissioned officers held commissions from the Crown. The distinction explains the administrative origin of the term warrant officer.