No. The ship itself if equipped with a donkey engine was Donkey Riding, while other ships not equipped with a donkey engine had to work harder.
The donkey lightened the load as Henry said, but it was the entire crew who felt the benefit.
Donkeys also enabled shipping owners to work their ships with less crew and so compete with all-steam driven ships for a while, until those ships engines became more efficient and so the days of sail were doomed to history.
(Donkey engines did not propel the ship, just the winches etc.)