It would work just fine, if everything ran smoothly.
My experience with foggers is always bad, mostly cause I buy the cheap ones that seem to break down within two months.
the problems;
-gotta spend serious cash on a good reliable fogger
-the fogger needs maintenance regularly
-the fogger can not fog every kind of nutes, expecially organic, forget about it.
-the unit should run 24/7, which adds to the power bill. on and off operations seem to kill the damn things
my experience... totally not worth it, I went back to aeroponics. I found myself watching the fogger unit every 12 hours, it became a real pain. And always got paranoid the damn thing broke down again and the plants were dying.