While the effect doesn't seem to be as noticeable with most film caps, electrolytics certainly benefit from some run time. Some years ago I recapped two Quad 33 stereo preamps. I listened to both right after the recaps and could hear no difference between them. Out of curiosity I let one sit unused and ran pink noise through the other for two weeks. I turned the burn in unit off for a day. I then turned both on and let them sit for a day just to make sure they were "warmed up". The unit which had been running with the pink noise sounded noticeably better (in my opinion anyway). Less harsh, more dynamic. After a couple of weeks doing music duty in my shop the "unburned" unit came into its own and sounded pretty close to the other.
I have noticed over and over that when replacing caps there does seem to be some improvement in sound over time.
But one does have to be careful in evaluating these types of things. The change can happen if a unit hasn't been used for a while and no parts have been replaced. Also, changes in line voltage and spectral purity of the line voltage can create a similar change (at my house there are big changes between daytime and late at night). What your ears have been subjected to before your evaluation can make a difference. And as mentioned above, your ears can adjust, giviing the impression things are better (you might be better off not listening to the unit while it is burning in to prevent this from happening, however your brain does not have very good "sonic memory" so you may not remember what you heard before properly). So as Fletcher says "YMMV".