Well, yes and no.
The story is not improvised as in, we know where we are, we know where we want to go and we know the major stepping stones of getting there. But there are also smaller steps in between that are evolving naturally or crafted along the way to serve a purpose (even if the purpose is simply "moar sex").
Same goes for the characters I would say. There are mainstay characters, there are secondary characters and there are fillers. One such filler character for instance would be the priestess.
She only serves as a carriage for the Temple bit and maybe look kinda hot in the process, but there aren't any big plans for her. Maybe she has an encounter with your penis at some point in the future, maybe not. Maybe we find out that she can actually be used for some part in the story and she makes a comeback, but quite unlikely.
There is also the notion of characters somewhat writing themselves, whereas you start with a character canvas in mind but as you develop them more and more they also steer bits in a certain direction.
Is something fitting with their past actions? Or the way they expressed in the past? Is it consistent enough?
I believe that those things are all part and parcel of the creative process of telling a story over the span of years. Some things are nailed down, others crop up "as we go".
That said, I do understand that some updates can feel disjointed due to the structure of the game, but hopefully it flows better as a whole.
I would argue that the world is the story in a sense, and the MC can influence how it unfolds. But it's not a "coming of age" story where the MC's growth is the focal point. He's just a medium to observe -or impact where you can- what happens around you (and score some booty in the process).
The world would change with or without the MC, maybe not in the same way or degree, but it would change.