It should work using a riser card to make a PCIe x8 or x16 card work in a X1 slot assuming your SFF case can fit it (doubtful), but it's not a good idea considering your old power supply which may not be producing any more than 200w at 12v. My advice would be to replace the entire system. There are boards like the GIGABYTE GA-AB350N-Gaming WIFI which are ITX so you can maintain the small form factor while having a full PCIe x16 slot for graphics.
Ok thanks for the information.
I plan to eventually upgrade the Thinkcentre to a later model, but am holding on to this one as I normally run at least two pc's. This one has a retailed licensed Vista x64 which is old I know, but works for what I've need to use it for. I guess after upgrading for more than 35 years I hang on to computer items as long as possible, putting some of it into storage, I tend to hang on to some of the older stuff. My first PC used 64KB memory and a 4.0 MHz processor, I've gone through dozens of PC's since.
What I'll probably do is look around for a PCI video adapter as it has a 32-bit PCI 2.3 (5v) slot. However higher memory and faster video adapter seem to be more difficult to find that use a regular pci and pci-e x1 slot. However I idid find a Zotac GeForce GT 710 that shows it has a PCI-E x1 Interface.
here's a pic of the actual slot, appears it's designed for other pci interfaces besides x1.
Zotac GeForce GT 710 DirectX 12 ZT-71304-20L 1GB 64-Bit DDR3 PCI Express x1 HDCP
It's new and they want $52.94. I was looking for something less expensive around $20.00 to upgrade a ~10 year old pc. But probably should just find two more PC's with newer architecture, better cpu, etc.
NVIDIA GeForce GT 710 GPU
192 CUDA cores
1GB DDR3 memory
64-bit memory bus
Engine clock: 954 MHz
Memory clock: 1600 MHz
PCI Express x 1
That' s not a PCI Express slot like any I've seen before.