No. This has been measured many times. Part of the myth is so you won't return it immediately and you'll get used to the sound of your new speaker.
There's a very long post at Audioholics, which I suggest reading the end first. They don't say driver break in isn't real, but that it happens very quickly and once it occurs there's no need for more:
In an electrodynamic driver featuring the usual surround-diaphragm-spider construction, driver suspension mechanical compliance plays a key roll in determining the measured value of various driver parameters. All of these parameters will shift as the mechanical compliance of the driver's suspension shifts in value. The bulk of a driver's compliance shift will occur at the time of initial burn in.
Subsequent shifts in compliance are largely temporary in nature.