Plants already love grey water as it often contains phosphates and nitrogen from lawn runoff.
Using uncontrolled water like that, especially if you're counting on it being contaminated with feed already, is a recipe for disaster. Some crops like tomatoes, cucumbers, zucchini/squash as examples really do not like nitrogen as they get into the fruiting stage. Too much and they'll remain in their vegetative growing state and just not bothering with the flowering and fruiting. You sometimes see that in ornamental plants too. Trumpet Vine is one that comes to mind. Too much nitrogen and it won't flower. Beyond that you would still want to sanitize the water. Grey water, I assume, would likely be contaminated just as much as surface water (ie: a pond) and therefore require a bit more work which is something I know about. I work in a greenhouse and I'm the guy that gets to muddle with ozone, chlorine, hydrogen peroxcide, or whatever else we're using to clean the water up. Failure to keep the water clean leads to, at least, clogging of irrigation emitters and at worst fungal diseases. Even if you're working with water so clean you could drink it you STILL generally put something in the lines to keep thing sanitary.