It's funny how often an artist asks if it's OK if they do an alternative tuning on a song... as if I'd get upset with them. There may be engineers who do, but I never have.
Drop tunings can change the emotion of a song and artist do that a lot. It can make for some mixing issues as the low bass notes take up the same space sonically as kick drum, but so what. That's for me to work out.
I came across something recently that I'd like to explore with artists. Most of the time A is 440Hz and everything follows that standard. But that's just since the 30's or 40's. Before then A could be 432 or 435 and I've read that A444 is supposed to improve sound too.
A 432 Hz tuning, is described as perfect because all the other notes stay whole tones. Middle C is 256 Hz, E above is 648 Hz. This stays consistent throughout the entire note range. With some tunings the other notes fraction off and supposedly our ears or brains don't like the sound. I wonder how digital treats that, but that's another issue.
This may be something or it may be nothing. Try for yourself. See if things sound better when you tune differently. And when you record, tell your engineer so he or she can work better with what your doing.