Isn't Merit a bacterial agent?
I probably wouldn't mix them regardless of whether or not a clear-cut reaction will occur.
I would do the heavy chemical drench first - since those usually have the most potential for damage as as well as typically the most effect - then apply the Merit with a single, high PPM feeding between them - one would assume the bacteria would hang out a bit longer in the medium and be more effective once the RA population is under control - but this depends a bit on the particular insecticide and I'm only familiar with
pyrethrin and
pyrethrin synthetics re: typical growroom breakdown times.
I understand you were not looking for another pesticide recommendation, but Insecticidal Soap Concentrate is really cheap (like <$10), particularly well suited to soft-bodied insects, and 40ml/gallon obliterated a RA problem I had over the past month. So, food-for-thought.
Good luck.