So I am currently thinking about getting a new graphics card for my desktop which I built in 2012. I currently have the gtx 560 ti and was thinking about putting in the new gtx 970. I'm not sure if running both of these together will be a lot better than just replacing the 560 ti since they are so far apart. Also if I were to use both of them would I be able to enable SLI, again since they're so far apart.
The only benefit you might get is you might be able to use the 560 as a dedicated PhysX card. But honestly, the 970 is a beast and I would just switch to it as your single GPU.
I went with the Gigabyte G1 Gaming GTX 970. Modded a custom BIOS onto it for 1202/1506 core and 3805 RAM. Still runs cool and quiet even with the OC, stays <66c and <65% fan speed. Going on 4 months now.
I would try to sell the 560ti on CL or Ebay as you should be able to get a decent chunk that you can apply to the 970. As mentioned, you can't set these cards up in SLI.
Another much more affordable option for you would be the GTX 960. 2 GB version is around $190 and 4GB is $220. Unless you are looking at getting into some more advanced games or higher resolutions, you probably don't need more than a GTX 960 which performs very similarly to a GTX770 which blows away the 560ti. Obviously the 970 is a much better overall card, but you may not even need it. Just giving you some options.
You can't run them in conjunction with each other at all (save for the afore-mentioned PhysX set up). You can have them installed in the same computer but running to different monitor set ups. The two will not help each other in any way.