I have multiple times heard this claim, from very different sources.
There certainly seems to be some correlation between intonation and "loudness", in the sense that ensembles with great harmony playing/singing tend to give an impression of inherent power – without needing any brute force or particularly loud instruments.
That sounds more powerful to me than a not-so-great brass ensemble, let alone any vocal harmonies that were severed with autotune. (Please nobody tell me 12-edo is good intonation!)
However, is there really any direct way in which good tuning makes a voice louder? At least if we consider loudness as purely physical power (Fletcher-Munson weighted or not), this seems doubtful: energy is conserved, it doesn't care whether frequencies match up exactly. So if there's any such relation, I suppose it would have to be a more complex psychoacoustic kind of loudness.
Does such a thing really happen, or is it merely the case that good players will generally have, apart from better intonation, also a "better tone" – which in itself already sounds subjectively firmer/louder, regardless of intonation?