I run El Capitan on a Quad Core 2008 with a Radeon 5770 and only 12GB of ram, and it's perfectly fine. At least, it didn't feel any worse than the prior OS and I think it's really fast. I did initially have some stability issues with random apps, but those were resolved with a fresh install and not migrating my user profile from a backup. (Instead I just copied back all of my documents manually) My machine has a 1TB SSD as the boot drive though. In my opinion, the SSD is what really makes the difference. The machine boots very quickly, apps launch quickly as well. Before I had an SSD it was much slower; I can't stand using a machine without one anymore.
So the answer your question, yes, it will probably run fine. But consider an SSD if you think your machine is slow, even if you have to buy a smaller one and keep your documents on a different drive. I use an Icy Dock adapter to fit the small SSD into the Mac Pro's drive bay.
I had hoped to replace mine years ago, but after the 2013 was announced I decided I would wait one more refresh cycle to see what would happen with GPU options for the 2013. Obviously nothing happened, but I'm ready now from an external storage standpoint so I can finally consider whatever they decide to offer this year.