Yes, they do. That's the entire point of breaking them in. I do so with every driver that passes through my hands because if not broken in the speaker will not work as intended. By all rights it should be done at the driver factory, and if not there by the speaker manufacturer, but break-in takes time, time takes money, and so...
There is a difference between manufacturing inconsistencies in T.S. Parameters between same model drivers and the differences that happen in one driver after a break in period.
These are two different things.
The type of mechanical compliance changes (though some individual parameters may be as much as 5-10%) basically equal out as far as performance goes. Box resonance and compliance has a great influence on the overall result too.
Not to say there is no noticable difference. There IS such a thing as break in from an unused driver. And over long periods of time I think there can be more change. I'm sure you have come across extremely compliant very old or "pounded" drivers. Especially certain surround, cone an spider types. Actually, I always thought that my foam surround Lowthers always sounded better just before they died. But this is not really relevant to the original context.