No need to run any form of car speaker in...
There is a break in period.
During this time the speaker will change it's properties. Which many people will say is its run in period.
As any mechanical device, start as you wish to proceed.
If your aiming for SQ when you first play it, the sound will change to say 2 months down the line or 100hours of use or whatever (it varies for each different speaker).
For SPL you may find in increase in SPL after you have "run them in". Basically the coils resistances will alter, as will the stiffness of the rubbers etc....
Normally softening of rubbers produces a much greater SPL!