Nope. While downstream by Yorkville I've heard of there being grass carp, I've never seen or caught any from the Fox. You're not allowed to snag in the Fox anyways.
The problem remains that you're only allowed to snag within 300 feet downstream of the locks and dams on the Illinois, which requires a boat.
You can't even use the Chinese fishing rigs for catching them on rod and reel because the DNR considers that snagging. I was told so by a game warden that I asked, and then he better not see me using one of these:
I think bow fishing is your best bet. I don't have the money or storage space for a bow suited to the job, but I picked up a fish spear for about 7 bucks. I have a mind this summer to take some powdered mashed potatoes to bring them to the surface and then have a toss with the spear. Kludgy, but you really just need to bag a couple of them to have some nice meat for the freezer.