Possibly, yes humidity will definitely get to the dry powder nutes if left open or exposed for even a few minutes. They come with bags that seal at the top, but I know sometimes these can not seal properly or possibly still leak a bit of moisture though.
You can tell when the humidity has gotten to the MEGA CROP when it clumps up (a bit like kitty litter?)

Good news is that it still is fully soluble in water once it clumps up, it just takes a bit longer and is messier. So, if you notice problems, I would see about switching to a dedicated container that is air sealed. I don't have that many problems here in San Diego, but its pretty dry. So, in humid areas it may be much harder to deal with, in this case you could just buy a container from Walmart or even just a 5 gallon bucket with sealed lid, and that should work pretty well!
Desiccant pack I do not think would be effective, since if there is a humidity leak, then the pack would lose effectiveness pretty quickly and you would have the sample problem.