The origin of Galactic cosmic rays (CRs) is unknown even though they have traditionally been connected to supernovae based on energetic arguments. In the past decades, Galactic black holes in X-ray binaries (BHXBs) have been proposed as candidate sources of CRs, which revises the CR paradigm. BHXBs launch two relativistic jets during their outbursts, but recent observations suggested that these jets may be launched even during quiescence. A0620−00 is a well-studied object that shows indications of jet emission. We study the simultaneous radio-to-X-ray spectrum of this source that was detected while the source was in quiescence to better constrain the jet dynamics. Because most BHXBs spend their lifetimes in quiescence (qBHXBs), we used the jet dynamics of A0620−00 to study a population of 105 such sources distributed throughout the Galactic disc, and a further 104 sources that are located in the boxy bulge around the Galactic centre. While the contribution to the CR spectrum is suppressed, we find that the cumulative intrinsic emission of qBHXBs from both the boxy bulge and from the Galactic disc adds to the diffuse emission that various facilities detected from radio to TeV γ rays. We examined the contribution of qBHXBs to the Galactic diffuse emission and investigated the possibility of SKA, INTEGRAL, and CTAO to detect individual sources in the future. Finally, we compare the predicted neutrino flux to the recently presented Galactic diffuse neutrino emission by IceCube.