Hm, don't know about crabgrass specifically, but some grasses are sensitive to salts in general. Here in FL it's accepted that you can't grow Bahia lawn near the seashore. So you can slow down if not outright kill Bahia grass by spraying with a salt solution (table salt). It does need repeating a few times to be effective long-term and like any herbicide, you gotta be careful what else you hit if you're spraying amongst flower beds for example.
I also use baking soda solution to prevent mildew and other fungal problems in my veggie garden. As far as the crabgrass goes, I'd say it can't hurt to try it! Use a mild solution - I use 1/2tsp. per quart of water in a spray bottle.
