Which Mac Pro version number is that? 1.1? It is possible to upgrade most (if not all) Mac Pros as far as I know, but I was referring to upgrading the ones from 2010 with 8 cores. That's a minimal speed bump at a ridiculously high cost.
For you it might actually be pretty awesome, but the upgrade is harder because you have to pretty much take apart the whole MP to reach the boards with both CPUs on them. Also, for some models Apple used CPUs without the usual metal cap - if that is the case, normal CPUs won't work because they're higher and you would crush the CPU and mainboard if you try to mount the heatsink on the new CPU.
There's a lot of info floating around if you google a bit. A starting point is here:
https://www.everymac.com/systems/apple/mac_pro/faq/
Go down to "Expansion and Upgrade Q&As" and look for your model. You got to be careful though, because the W3*** CPUs won't work in the Mac with two CPUs.
This could be the one for you:
https://www.everymac.com/systems/apple/mac_pro/faq/mac-pro-how-to-upgrade-processors.html ?
Video Part I:
http://www.youtube.com/watch?v=wmz7gPw31L0
Video Part II:
http://www.youtube.com/watch?v=phzn8MPaDtQ
Personally I got my info mostly from these threads:
http://forums.macrumors.com/showthread.php?t=1120326
http://forums.macrumors.com/showthread.php?t=1122551
They can help you visualize some of the necessary steps but getting the tray with the heatsinks, CPUs and RAM out of the MacPro is a lot harder with your version.
Fwiw, I did the upgrade today and it took me less than 30 minutes. Almost doubled the performance in the Geekbench score, from 8870 to 16118 points.
http://browser.primatelabs.com/geekbench3/441952 This puts me somewhere between the 2009 and 2010 MacPro 8-Core