That would mean the owner pays for the survey, and gets to pick their own surveyor, and since the surveyor is working for them its not necessarily to the benefit of the buyer. If the buyer pays for the survey, they get someone working for them to identify everything that's wrong.
Regardless of whether the seller or you pay for a survey of a boat not under contract, the seller could sell to someone else after you paid for a survey wasting your time and money. It serves no purpose for you to survey a boat prior to agreeing to a price and signing a contract
If the seller is paying the surveyor, you can bet your rum that he will find a few little things, just so the buyer would think he did the survey. Depends on how "uninformed" the buyer is. Otherwise, CYOA.
A recent survey done for some other purpose, such as insurance, going off shore, etc is available then certainly it may help justify the asking price and provide some guidance for a potential buyer. Paying for a pre-sale survey for no particular reason other than selling the boat just adds to the selling cost. Which can get steep quickly depending on the buyer's survey.Survey's are done for several different reasons. Sometimes your insurer might want one (cynical aside: a friend in the industry sez that often they just want to be certain that the asset actually exists...)
Good luck and I hope that your current good survey helps to enthuse a new prospective owner.