No that won't be a problem. When you take Miracle-Mineral-Supplement , it goes to the stomach, that is where the blood vessels absorb oxygen and a lot of your nutrients. Since the body doesn't have many mechanisms for recognizing the difference between oxygen and chlorine dioxide, the red blood cells will pick up chlorine dioxide. It will then travel through the blood stream to places where oxygen is released to oxidize poisons. It will interact with these poisons in an explosive manner with about 100 times the power of oxygen.
The vitamin C is an antioxidant. If there is still chlorine dioxide that hasn't been absorbed in the stomach, a large dose of an antioxidant will neutralize a lot of it. If it is already out in the bloodstream, a fair amount can be neutralized. In the stomach, if there is fat or something slowing the digestion, Vitamin C is going to be slow to get into the bloodstream. If your Miracle-Mineral-Supplement dose is at the height of its reaction, C can't stop what has already been set in motion in a vascular area far from its entry point into the bloodstream.
The main thing is that since Miracle-Mineral-Supplement is 100 times stronger than the normal oxygen that is usually picked up by the red blood cells, oxidation will not likely be impacted much by incidental ingestion of a food or juice with a normal content of C. But to supplement C or stop a detox reaction you will need grams of C not milligrams.