This is my experience with using hay for fertilizer: I bought a place a couple of years ago now and to say it was in bad shape is a gross understatement. It's still in bad shape but miles ahead of where it started. I didn't need lime, the PH is perfect for pasture, but it needed fertilizer. I toyed with the thought of dumping the rates recommended by soil test on the place but that is expensive and I just didn't see where fertilizing weeds and bare spots was going to produce anything above foreclosure.
What I brought with me to this place was basic knowledge of how to grow grass and many other plants that I gained through experience. I have fed hay in rings, grazed bales, and rolled out hay (by hand). Most all hay has seed in it and that seed will sprout given the right conditions but it needs water to grow. A hard packed bare knoll will not grow anything if it can't hold water. A thick layer of organic matter (hay) will not only hold water but makes excellent sun screen for the soil.
Someone already mentioned weeds in brought in hay. When you bale graze or feed whole bales, the weed seed is concentrated in one spot. The sprouted weed seed isn't a bad thing on bare ground because they will help you get to where you are trying to go. Just never let the weeds go to seed. If they are concentrated in a spot they are easier to clip and manage. I found that I can knock down weeds, spred thick spots of hay, and spred manure in one pass with my cutter in the spring after the weeds and grass seed has sprouted.
I spread chicken litter over the whole place last spring. It did absolutely nothing for the areas that were still bare and couldn't hold moisture. The areas where the soil was newly cleared and the areas where I fed hay bales to build organic matter, did wonderful and didn't show near the stress from the fall dry spell as the rest of the pasture. I personally wouldn't spend money on synthetic fertilizer, unless the organic matter is where it should be first. Our streams don't need it.