most interesting topic. The answer is that the sheep can both speed and delay replenishment.

If properly rotated in paddocks, grass will grow more biomass. Part of it is the relatively evenly spread manure, and part is the decay of trampled grass, which is processed in an accelerated fashion due to the simultaneous injection of manure (bacteria).

If left too long in the meadow, the sheep could end up overeating the grass until tillering is no longer possible, and now you lose organic matter and therefore topsoil. You can spend hundreds of hours on youtube, by author (Gabe Brown, Allan Savory for example), topic (rotational grazing density, holistic management), or institution (SARE, NCATATTRA).

Basically, so long as you mimic the natural prairie ecosystem, you build soil.

Somehow I got myself thinking in another direction: Energy to build topsoil comes from the sun via photosynthesis and plant decomposition. The sheep consumes some of that photosynthesized energy (grass) and uses a part of it for metabolism, CO2 expiration, etc. Then the sheep becomes a net loss in the chain from sun to topsoil, in other words, it uses up more resources than it gives back. In that case, the energy used for metabolism and respiration would cause soil to build more slowly than if the sheep wasn't there.

Am I off on a wrong track somewhere?

It is not a simple answer - this is a pretty complex issue. One of the better explanations I have encountered on how grazing and soil building can work together, much like glib described, is contained in this article: How to build new topsoil. But it doesn't take much of a diversion to head in the opposite direction either :-)

you are on the wrong track. soil builds faster in the transient presence of ruminants. Savory was a park administrator in Zimbabwe and could see that himself. IMHO, the effect is biggest in semi-arid climates. In a climate with a lot of rain, it probably makes no difference (then again in a rainy climate we usually have forests).

I have no doubt glib knows his stuff on this. Also not surprised that the way nature was originally organized turns out to be optimal. It makes sense that there is a point where the overall metabolism rate of the system results in maximum utilization of available resources. A saddle point between resource extraction, microbial growth, and decomposition. Change any of those factors - harvest manure, grass or meat for example - and it may no longer be optimal. By the same token you could also boost something - adding organic matter, microbes, nutrients, water - might push it to higher production, but only up to a point where some other factor becomes limiting.

Amazing how nature do dat.

I would think it would depend also on the number of grazing animals and the amount of land. For instance just one animal could never overgraze a big enough area. It would simply keep all the grasses trimmed back and help enrich the soil, attracting microorganisms to the manure and the area in general.

Two points - first sheep (and other grazing animals) are composting machines. That's essentially what happens in their digestive tracts. Carbon and nitrogen rich material is combined with bacteria in an accelerated environment, before it is expelled partially composted. What might take nature six months to accomplish happens in a couple of days in the animal's gut. This is the advantage of feeding grass to a sheep or cow vs. just letting it drop on the ground.

Second, the grazing animal will change the flora of the meadow from a grass land to perennials and shrubs by consuming the fast growing annual grass and leaving room for second-stage succession plants to take over. This could hurt the soil building by preventing what would normally be decades of composted grass buildup before it slowly transitions to shrubs. Of course the manure helps, but that is a short term benefit vs a longer term benefit - so it depends on what you are trying to accomplish and when. And how many animals you graze - if you rotate over several fields giving each one time to recover, then then you prevent the premature succession to hardy perennial plants. (And leave food available for future sheep.)