Yes on the FHM if the water hasn't dropped a lot (40%-50%). I woldn't do the hay thing, that'll just be more organics in there. The jury is still out if hay works on all ponds. I've seen where it does work, and where it didn't do a thing. With all the leaves that will be falling shortly, the pond will have plenty of organic material in it within the next month.
Getting the grass seed down and established will do more for the muddy water than bales of hay.
If you can get to the water, and get a mason jar full without scraping up mud from the bottom, do it. Set it on the counter for a few days without disturbing it. If the clay settles out, then you're fine. If it stays in suspension, then the pond will need to be treated with alum/hydrated lime to balance out the electrical charge in the water and precipitate out the clay. But, wait until you have grass growing around the pond to prevent more clay from washing into the pond first.
