I've only run a little but it's sort of amazing what does and doesn't come through in a distillate. Open fermentations using a lot of corn can get pretty nasty and the resulting distillate needs serious aging.
I think as long as it's good barley malt or even malt and sugar, the hop and yeast contributions can add interesting notes without getting in the way. Now if you run deep and include the 5% alcohol swamp water at the end of the run when you do the blending, you could end up with some pretty funky flavors. Even then, if it's aged for long enough on good oak, that nasty funkiness turns into "complexity".