No! Tbh in all my research, study, texts, etc I have never seen it mentioned any (negative or positive) effects when vitamins and MDx/LDS are combined (deliberately in cases of assay/research or by consequence as in your situation).
I am confident there will be no issues.
Just as a random tip, unless one has been specifically told to take a vitamin/multi-vitamin - by a health professional from a GP, Nutritionist, a Dietitian where specific test have been done and there is provable, shown reduction is a vitamin - they essentially become what I like to call "expensive pee"! The body retains stores of very few/specific vitamins for later use and if one is required the body will follow processes to obtain them (make you hungry, synthesise it itself). Therefore, unless one is actually deficient, the body will end up expelling it as (unwanted) waste.