That's not true in any meaningful way, as far as I know. I took several years of Mandarin courses, and there were exactly zero times I was able to guess a pronunciation from a radical... and I'd learned 1,000+ characters by that point.
Perhaps that's true in some areas of technical vocabulary? Or there are a handful of examples that have the same pronunciation. But I'm pretty sure that trying to guess a pronunciation from a radical, you'd be wrong 99% of the time.
Note that when we survey the multiple dialects in China, we see that they more or less preserve the Middle Chinese 4 tones, even though the tones' realizations have evolved so greatly such that the Middle Chinese tones' actual realizations are but unreconstructible.