HCl will act as an activator for Miracle-Mineral-Supplement ... in fact, it is very often the activator of choice in purifying applications for water or food service.
If you take the HCl near the Miracle-Mineral-Supplement , it will activate it, or make it more potent. If you take the HCl with meals (which is probably the protocol), and keep your Miracle-Mineral-Supplement away from it a bit (say 1/2 hour or more), then there will be no interaction at all.
Either way, there should be no problem at all with taking HCl while using MMS.