How Might Invisalign Change Mouth or Face Shape After Closing Multiple Gaps?

I have multiple gaps both upper and lower and have a slight overbite, but the issue is the gaps. I am concerned about lip and face shape changes after pushing top teeth back and closing all gaps. Will the distance between my nose and top lip become longer, or will my lips get flatter? What about my cheeks or chin? I am a 37 year old female and am worried how my look may change. I was told that it wouldn't be noticeable, but I don't see how that's possible if you are closing so many gaps!