It is my understanding that barleygrass is grown the same as wheatgrass, which is grown in soil to get the healthiest growth and thus maximum nutrients into the juice. Yes, you could likely get it to sprout and grow without soil, but it would lack the essential nutrients to flourish, and to impart those nutrients to you when you drink the juice. Or you can just sprout the barley with water and eat it as sprouts.
If you wanted to experiment with growing barleygrass soil-less, I'd say at least water the seeds with some kind of nutrient-rich compost tea, and provide a medium, such as wet paper towels for the seeds. No guarantees though. Maybe someone else has more experience on this...
