From my experience:
T05 - was too fast first 2-3 training sessions or like 4-5 days (or maybe ~10 hours if that was more important), then it was ok for ~7 weeks. I'm sure that there was speed drop in initial period, which slows down after first week, not only my adjustment to it.
Acuda S1, Hexer - those are weird rubbers for me, they are the only rubbers that I really liked to glue on a blade and go to tournament the next day without any training. They felt fine for me for first 1-1.5 weeks (didn't play a lot those days, maybe 7-10 hours of play), not so good after that.
MX-P - similar story to T05, maybe 1 training session it was somewhat faster than I wanted it to be, then was more stable, but here I felt that it changes steadily after that initial period, not only in terms of speed, but in terms of sponge changes, maybe softening,
MX-D - I use it on bh side now, I have less feeling there, so actually I'm not sure here, and it seems to me that it also changes gradually week after week, and it is more about difference between sponge of old rubber and a new one (but it also might be to the fact that I play like 3-4 hours/week vs. 15-20 hours/week when I used to play with T05)
K3 - it is slower than usual for first 1-2 hours of play, guess it looses some tackiness and hardness and gets more speed after it
Don't remember how it was with other rubbers I played
So under breaking in I mean quite quick changes to rubber in first period of its lifespan, getting more stable period after that. And in this case, I believe it exists (yes, for sure, I didn't measure it with any equipment, and not really going to do it). More noticeable for me on T05 and K3 and the more hours/week you play, the easier is to spot those differences.