They did. The HMS Swiftsure that was part of Nelson's fleet was commissioned in 1804. An earlier HMS Swiftsure was commissioned in 1787, was captured by the French in 1801, and fought with the French at Trafalgar where she was recaptured, recommissioned, and renamed HMS Irresistible.
I thought it must be some scenario like that. That era, particularly the naval battles of the Napoleonic Wars, was rife with ship captures and nautical prize-hunting.