A couple more thoughts... is the rough side of a leather strop useful for anything? Can compound be applied to both sides of a fabric strop?
The rough side of leather is often, “rough”. So, depending on what you plan to paste it with, yes you can smooth it, but a separate smooth substrate will produce a finer finish, especially with, nano grit paste.
Yes, I paste both sides of paper strops with nano grit Diamond and CBN for years. The problem with a nano grit strop, is contamination. Once contaminated with airborne dust larger than the sub-micron grit/paste, you are imbeding stria to the bevel and edge instead of polishing the bevel and straightening the edge further.
A lot depends on what your intent is, at what level, you want to polish.