But as said many times over, there's no room for a Captain's Yacht in the TV show. Either it would have been shown whenever Picard travels, or then there are pressing in-universe reasons why Picard can never travel on it so it cannot exist.
There's nothing on the bottom of the saucer that would look the slightest bit like a "yacht", so that argument is moot as well. The only way to believe in the Yacht is to claim a priori
that it exists, and then start seeing it everywhere or invent reasons why it's nowhere. Which we can do e.g. for things Paramount could not afford to show "for real" but did mention in dialogue. But the Yacht isn't one of those.