Voted yes, but it's exaggerated, hugely exaggerated.
I’ve never experienced any changes beyond the first 24 hours of run time if that and with the vast majority of phones nothing changes from the first point you plug them in onwards.
The most severe burn-in experience I ever had was with the TMA-1 that sounded completely different from first fire up and an hour later, although I suspect something more physical could have been the cause, like maybe a bit of something stuck to the driver that dislodged.
Many people confuse the process of getting used to a sound signature with burn in and post these huge detailed burn-in sagas which really just chronicle their subjective experience of finding a new sound strange through to normalising and then enjoying it.
There is also the fact that if you beleive in burn in, you will experience it. The mind works that way and is perfectly cabale of making something sound better over time if you expect it to.
There are also other factors like reduction in clamp and compressing ear pads which would make it seem like the drivers were changing over a longer period of time when the changes are actually acoustic.
One thing that is pure snake oil though is when solid state amp manufacturers tell their customers their amp needs 100 hours burn in to sound right, ensuring they either get used to its defects or expire the returns period. Anyone telling you a solid state amp needs burning in should not be trusted further than they can be thrown.