Generally its the delivery crew who use the sails to get the boat to where the rich guy wants to sail from. Often the crew are given a budget, for all expenses including fuel, and so anything they save on that means they have more spending money for more vital supplies like beer, beer and more beer :-)
These crews move the yachts around the world as "the rich guy" wants spring in the Caribbean, summer in the Med, fall/autumn in the Indian Ocean, winter around Australia. So you move the yacht to meet the guy and his family/friends for the holiday onboard at specific times.
You use the diesel engine when you're likely to miss the departure/arrival dates.
Its a fun life but badly paid, but you get to spend your time on a luxury yacht.