I'm still new to this, but I think you can desulfinate one at a time. While I'm still deciding on several products, I will hook up a desulfinator to one battery and not the other one. At the end of the test period (4 weeks), I will compare if one is better than the other. If I get positive results, I will do the other one.
I think you can still charge while desulfinating. I think the desulfinator is capped at 12V so hooking both up and desulfinating will overload the unit.
Will keep you posted...