Absolutely NOT! I was realllllly concerned about formal nights on our first cruise and our T.A. kept telling us not to worry. ! The worrying was for naught. While you'll see a little bit of everything on formal nights, you'll not find yourself to be "over dressed". And on the hand, we've seen folks who wear their "Sunday-Go-To-Meeting" clothes - and they look great too.
Do not, repeat: DO NOT waste one minute worrying about formal night. You can dress up "to the nines" and fit right in - or wear a nice dress or fancy slacks and top and you'll fit right in.