From what I've read so far, it depends. Some speakers might have a brittle edge to them because of the components, stiffness as a result of the manufacturing process or any amount of other reasons. As the cone and coil moves, they relax within tolerances over time. Some might not. I guess the questions are: Do you want the broken in tone faster, or do you want to enjoy the entire breaking in process of the new speaker? Some more experienced fretters may chime in on this. The article from PG linked above explains it really well.
Personally, I would like the broken in tone of the speaker as fast as I can so I can evaluate my amp easily. May not be necessary but might be worth looking into.
FWIW.
“Your sound is in your hands as much as anything. It’s the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use.” Stevie Ray Vaughan