I have enough of a scientific background to know that you need to change just one variable at a time to avoid confusing results, so I adhere to that sort of scientific discipline.
From my experience, I would say that generally I have heard improvements immediately from changing some components, but that there can be additional improvement over time. One instance that has surprised me was having my Apogee Duetta II (with ribbon midrange-tweeters) speakers refurbished. The man who did the work said there would be a break-in period of a few hundred hours. But I found they improved after about a year of regular use--there was some brightness that gradually diminished, and I could test this with one particular piano note on one particular recording, as well as massed violins in some orchestral recordings. So, that’s another way in which I’m disciplined--like many audiophiles I rely on certain familiar recordings for testing components.