I read in another forum that NIC cards can be run on PCIe x1 slots. Is this true? If so, can a Wireless NIC be so run? I have a Linksys Wireless-G 54Mbps card in my PC right now running off the regular PCI slot, but I only have two of those and it would be nice to free one up and use the otherwise seemingly useless PCIe x1 slot.
No, they're not directly compatible and interchangeable.
The situation with wired gigabit NICs is that some of them come in PCIe form factor, and can also usefully benefit from the additional bandwidth / avoiding crowding the PCI bus further in some cases. But even then the add-on PCIe GbE NIC market is pretty small.
I'm not aware of any wireless PCIe cards, and it couldn't benefit from the bandwidth in any case.
Another alternative for saving a slot would be to use USB or a wireless bridge.