Well, QnD obviously isn't SV, so you are simply planning on doing QnD alongside Reload but without the SV option. And the QnD books says that you should be fresh when doing the workout. So it probably isn't a good idea to do QnD after a barbell session.
That being said: QnD is said to be a minimalist program that allows you to pursue other goals and SV is optional on the Reload program. So as long as you get enough rest and don't do too much too soon you can probably do them alongside each other.
If you want a more detailed answer (ideally from someone more experienced) you should probably give some more info. Age, lifts, current training, what you actually intend to do (there are several options in Reload on how to set up your program).
I do a 1 on/1 off Reload program without the SV option (but with row or chin ups every workout) and jump rope training on off days for conditioning and I definitely need my rest to recover. I think I could adapt to something like QnD if I drop the jump rope training. But I would only do it twice a week so I can get at least 1 full day of rest.