You betcha. The only reason for the soil is to provide an initial population of microorganisms to do the composting. Once they've populated the bedding, the only reason you'd have to re-do the soil addition would be if you did a total cleanout. I would emphasize though that you have to have the litter pack in a plausibly-compostable state for this to work... just chucking a coupla shovels of soil into a newly-bedded coop full of brand spankin' new pine shavings would be pretty pointless.
When you used this with horses, did you notice a change in the smell of the stall? I am wondering if this would also work with goat sheds on concrete.
The stalls in question did not really smell (at the surface) to begin with, so, I couldnt really speak to 'change in smell'.
It *should* work with goat sheds on concrete, although remember that if the litter pack has been there long enough it has likely cultured up its own composting microorganisms already (goats track mud in on their feeties...) So if you are keeping your goats on deep litter, but are not satisfied with the composting of the litter, you could try it. (Honestly the goats I've known have been kept on bare concrete for their indoor housing... but that was down South, and I'm sure there are lots of other maybe better ways of doing it)
I should add that I have rather mixed feelings about this whole "composting-in-place old-timey deep litter" thing, especially w/r/t backyard type chicken coops... in my experience it works well for horses if you have oodles of ventilation, but even if you do, it is somewhat on the dampish side, and I think in a lot of coops in a lot of climates you could run into problems with that with chickens (especially with subfreezing temperatures). Although I fully expect that there are situations where it works fine.
Personally, I use what I suppose you would call a deep litter system but keep it considerably too dry to really do a whole lot in the way of composting in situ. I only clean it out (usually just partly) if it gets too broken-down and dusty, maybe every year or so but it's an eyeball thing not a schedule thing. (I have tried adding some soil, btw, out of curiosity; it made no obvious difference, although of course it gave the chickens something to poke at for about five minutes
). This saves me having to worry about the moisture issues and I'm pretty happy with it. But of course everyone's situation is different.
Pat