You can, if you have an original Apple-branded NVMe drive from a Macbook Pro or Air. You can buy a special PCIe adapter for the Apple drives from AliExpress for a few dollars.
To use a generic NVMe drive you would need to install macOS Sierra or High Sierra. They require the SSE4.1 instruction set that is missing from the
Woodcrest and
Clovertown Xeons of the Mac Pro 1,1 and 2,1.
You could try putting a 5400-series
Harpertown processor in the LGA 771 socket, but the Mac firmware will not chime or post with the processors. So far no one has figured out what changes would need to be made to the firmware to make Harpertowns work.
There is however
a patch to El Capitan that works with generic NVMe drives. It has never had much use, as it came out at the same time as macOS Sierra with far better NVMe support.
back in the days when we had no nvme firmware it worked, so give it a shot.
Yes, using a fusion drive to boot when the system cannot boot from NVMe is a good idea. I
use it myself. But you also need operating system support for NVMe drives, which El Capitan and Mac Pro 1,1 lack.