The Three-fifths Compromise certainly came back to bite the South in the long-term. For example, Virginia which had one of the largest populations in the Revolution at a total of between 447,000 and 538,000 (a fair amount of these individuals were slaves to be fair) and by the ACW it had 1.59 million in population which included about 1.1 million free residents and nearly 491,000 enslaved people. By comparison the state of New York had apparently somewhere between 162,920 and 210,541 residents in the American Revolution but by the Civil War had 3.88 million in its population (quite a few were immigrants) and no slaves to worry about electorally.
Perhaps I was confused by the phrasing of "non-citizens getting representation rights" considering that the legal doctrine of the country prior to the American Civil War and the Reconstruction Amendments was that "persons of African descent cannot be and were never intended to be citizens under the U.S. Constitution" according to the Supreme Court decision in the 1857 Dred Scott case.