I ran some tests where I mixed up a dose of Miracle-Mineral-Supplement , then added alcohol to it. The addition of alcohol did not decrease the ClO2 in the solution.
However, as you brought up, if alcohol inside your body increases the pathogen load, then it is possible that the extra load could neutralize the Miracle-Mineral-Supplement dose. Your perspective is more inclusive than mine was.
All in all, it is probably not a good idea to drink alcohol while taking MMS, even though the ClO2 in solution is not used up by the addition of alcohol to it.