Not quite. Pick any adult game. Go fresh browser/incognito without being logged in. Type exact game name and search. You will not find that game. Even though you explicitly looked for it, even by name. You cannot even find the creator, if you search for the creator by name.
The need for account and option toggled on prevents you from accidentally browsing adult games. Even if you type them by name or use any of the adult tags. You only get there by direct link. That is the expeced behaviour.
It does works for a tag like "sex". Try it out. You can find around 70 game with it, that are not marked adult - because they are not adult games. They just have that adult sounding tag. Tags are irrelevant for marking as adult. You do not even need any tags at all. Marked as adult is not the same as tagged as adult. I made a thread about this https://itch.io/t/2892152/make-marked-as-adult-a-searchable-tag
The expected behaviour is circumvented by selecting tag adult. Or nsfw and some others. Suddenly you see all the games in browse, even without an account. Providing you with the direct links you need to access them. Just re-read the response from no time to play. No login, no nsfw games - but this is not, how it currently is. If it were intended behaviour of the site, I expect he would have known that exception: that you can still browse for adult games by selecting some adult tags.
And if that is really intended, it should change. You might equate searching for tag adult with giving ok to see adult content, despite the option being off in settings. I do not. Having one clear setting and then circumventing it kinda , is very bad design. There is a reason that setting is buried ... well in the settings and not some toggle button in browse. And if you only need select tag adult, it becomes some button in browse.
I dimly remember browsing on itch last year when I did not have an account. I could not find any adult games back then. And I am pretty sure, that I tried the tag adult, because, you know, it is in the list and starts with an a.