Don't do it - at least not unless you can get a better sprayer than mine, which spit out big fat drops along with the fine mist, and wherever a big drop hit the drawing turned super dark. So glad I took pictures first! I decided whst the hell - it's either going to lighten back up as it dries (yeah - sure it will.. ) or it's ruined now, so I went ahead and soaked it pretty good. It turned black, as if all the white chalk just went totally transparent.
Maybe the way to 'fix' chalk drawings is to take a good digital picture and then just throw away the original.
Going through a bunch of boxes and my old school portfolio yesterday I ran into a huge mess of charcoal dust and pastel dust that's essentially ruining all the drawings in that protfolio and gets all over my hands. Yuck!! But today I was looking through the Pen and Ink Book and found reference to using skim milk as a fixative. Apparently Van Gogh used entire glasses of it to fix his pencil drawings. He liked the matte finish it puts on heavy graphite marks (interesting).
Here's an article about it: http://ryanmcjunkin.com/using-skim-milk-as-a-drawing-fixative/
Need to try this out. Much cooler than spraying aerosol cans of toxic fixative.