depends on what one calls simple

there may be some simple tests for increased soil fertility as compared to the reference soil w/o conditioner

but there are surely no such simple tests for carbon sequestration

furthermore, pertaining to carbon sequestration the question is not clear in many ways (e.g., which time periods are you considering)

you know, one expects some kind of fertilzing effects from the decomposition of organic matter OM such as sugar cane residues

but then, these may also excert a positive priming effect (increased degradation) on native SOC

if you want to add C to your soil you might want to have a look at the paper by Quirk and colleagues           DOI 10.1007/s12355-012-0158-9

or maybe mix carbonized residues with non-carbonized residues,     although results would be probably more complex than simply adding to existing fertility and SOC status

also, dont understand how soil erosion fits into the issue?

carbonized OM or not, in both cases I doubt that it would decrease the "erodibility" of top soils

you assume that by-products would reduce soil erosion?? is it tar-like?