Can Ubuntu use PCI-E SSD as a bootable?

On the whole, yes.

That is not to say that all drives will, or that it will be universally simple. I say that last bit from direct experience. Several years ago I bought a Ocz Revodrive. This was two fast SSDs strapped together with a RAID-0 chip on a PCIe x4 card. It was super quick for its time. Anyway, the complications of software-aided [fake]RAID meant that I had to make sure that the dmraid module was included in initramfs. This was not immediately obvious to me, nor was it simple.

Mine worked, but there are some cards with complex setups like this that don't have Linux drivers (few and far between given storage on Linux is their primary business). I would advise you Google for model-specific issues on Linux before purchasing.

Should also point out that if the drive works but (eg) you can't get BIOS to point at it, you can always install /boot on another drive. Even if that's a dirty little USB stick in the back of the PC. You have options.

I have since upgraded to nice simple —and very much faster— m.2 NVME card. I mention it because it's still technically PCIe. It works perfectly as the primary boot disk.

Since your motherboard has no m.2 slots, that eliminates the easy way to add a PCIe drive.

The SATA controllers it has do not support NVMe PCIe drives, the second easiest route to add PCIe drives.

Therefore, you must find a PCIe NVMe controller card to run an NVMe PCIe 2.5" drive, or a combination card where the PCIe drive mounts on the PCIe card. I would be very careful to explicitly say this to the vendor: "This is a condition of sale; will I be able to boot from your PCIe {whatever}?" If they do not immediately say YES, walk away.