So you’re suggesting injecting viral miRNA into the epididymis of parental mice and checking for symptoms of viral infection in the offspring? This won’t work because (a) the miRNA isn’t the whole virus, it probably won’t have a clearly discernible phenotype; and (b) the mechanism suggested here relies on specific vesicles. Export of small RNAs into vesicles isn’t an automatic process, it requires active targeting of the RNA inside the cells for export (RNAs essentially need to carry a “luggage tag” that directs the cell machinery to envelope it with a membrane and send it out).

Still, your fundamental idea has some merits. A more promising experiment would forego viral RNA and instead mutate the specific miRNA-206 in mice to carry a specific signature. Sequencing the resulting embryo in early development could show whether the mutated miRNA was taken up. I say “could” because there are fairly big caveat: miRNAs are short-lived (unless they are actively regenerated) and the concentrations may be too low to pick up a signal.