Will pci express x 1 work in a x16 slot?

The answer after this one is absolutely incorrect. A PCI-e x1 card is absolutely compatible with a PCI-e x16 slot, regardless if it is a rev 1.0, 1.1, 2.0, 2.1, or even 3.0. It is indeed smaller, but that's one of the main reasons the ground pin / physical notching is present on these cards. It is safe to install so long as it is anchored.

x16 is compatible with x8, x4, and x1. It is this way, and it has always been this way.

----(Previous, incorrect answer)

No, it would be too small and may damage your motherboard and card.