#1, no your water activity will not change (that's inherent based on the recipe)
#2, a humidifier works basically the same way as more humid air will always feel cooler (difference between winter in SW Ontario and winter in moosejaw LOL, both are -30 but one feels mighty cold compared to the other)
I'm guessing it has been chosen because A) it's cheaper than AC to run, B) they work best in hot dry environments. I would be putting a humidity reader on the production floor somewhere just so you can monitor any changes. I'm thinking about quality too.....if you make a crisp finished good, how will the relative humidity change affect the amount of time you have to get that product in a package before it starts to soften?
The real risk here is the unit becoming a breeding ground because it simply isn't cleaned often enough.....you could end up breeding yeasts/mold and pathogens which will shorten shelf life at best, and contaminate your product at worst
SQF can't approve to disapprove of anything. Period. Do not let anyone tell you differently. GFSI programs are designed to help ensure you are producing a wholesome product, it is up to you to do your research and implement controls if you think something poses a hazard.