No. You must submit your citizenship document before Election Day to be eligible to vote, if your status is still incomplete.
Once you are successfully registered, you do not need to bring your proof of citizenship to the polls. Once the citizenship requirement is satisfied, you do still need to provide your government-issued photo ID (such as your U.S. passport) in order to successfully cast your ballot at your polling location. Valid forms of photo ID are listed here: Voter ID Requirements (PDF format).