Yes, absolutely, choices have a big impact in the game. Some of them really shape how the story plays out.
We're still early in the game, so it might not always be obvious yet, but a lot of choices are saved and tracked behind the scenes. Some consequences show up right away, others only later.
About your example, yes, refusing the threesome can close certain routes and open others.
For example, I already mentioned this in the shop, in version 0.10.0, there will be a romance route related to Acasia. Not every player will technically get that romance or that part of the story, because you need to have made a specific choice at the bridge to unlock it. That will probably need a clearer explanation later int he devlog, but going forward, more and more story content will be developed differently depending on earlier choices. Some parts of the story will be more developed than others depending on what you picked.