I think the question has already been answered as to if it will work. Here is what he asked however.
Will a PCIe 2.0 x1 or x4 SATA III controller card work at full speed in a PCIe 1.0 x16 slot?
I'm going to with no, sort of. Will it fit/plug in, yes. Been answered already. I'm assuming you are replying the way you are because you want to know how much slower it will be in a 1.0 slot. This is hard to answer because bandwidth != speed. Just because you are on a freeway with a 65MPH speed limit doesn't mean you can go that fast. (like your 35MPH top speed moped.) You'll be fine with normal hdds, but SSD read/write speeds will be very limited.