I do scratch build in an apartment. Never had a big scroll saw, but a benchtop bandsaw (Proxxon MBS in my case) is not too bad. It has a bit of a high-pitched noise that does not travel too far (tested with neighbours), and I also put a rubber mat under all machines to reduce the noise distribution through vibration. You can buy these mats for washing machines and like.
So unless your apartment walls are made out of paper (which might happen) - it should not be a thing preventing you from scratch building!
Also the actual cut time is miniscule, you spend way more time preparing, marking up, gluing, sanding, etc, than the actual "cutting pieces from wood" time.
Would be happy to help you with any other "tools in an apartment" problems, there are some photos in my build log that might help It is absolutely doable! And you don't need too much space, my modelling corner is 120cm wide.