It will throw off the proper pistonic motion, which is never really perfect to begin with. In other words, the sound wave propagation will be distorted.
What does a uncentered speaker sound like if you refoam and don't get the cone centered.
I did a set of Advent babys a while back. One sounds great the other has a sound like a cracked speaker when the base is higher. I can not find a crack in the paper cone so I am assuming I did not get the speaker centered. Next time I will use the tone method but wondered what it sounds like when an uncentered speaker is used.