I suspect there's something to this. I find with guitar you can do something similar if you tune by ear, getting the strings to resonate with each other rather than perfectly matching a tuner. To my ears it produces a richer sound.

yes these are called sweetened tunings.

apparently it's often done in pro recorded music.

my peterson tuner actually has these tunings embedded inside.

https://www.petersontuners.com/products/strobostomphd/