is battlefront ever going to be compatible with a GTX 560 Ti?

You used an inapplicable term in your question's subject, so I altered it.  Your GPU is slower than the minimum, will always be slower than the minimum, and won't magically pick up any speed in the next month, when the game arrives for play.  It surely is able to "play" the game, although at a slower frame rate, or a lowered screen resolution, one or the other.

Meanwhile, there is not a current condition supporting any refund, since the debit won't come out of your account until a couple of days before the release, so if you cancel your pre-order, that will be the end of the transaction. 

http://gpuboss.com/gpus/GeForce-GTX-660-vs-GeForce-GTX-560-Ti

If you did not place the pre-order with Origin, the situation will differ, of course.

I spoke with a very kind person at EA Customer Experience and she agreed that my (overpriced) rig was incompatible for this game.  I was given a full refund.  Thanks for trying.

GodRex

It runs fine for me at 60fps if I turn the settings way down. Your CPU is probably bottlenecking if it doesn't for you.

My specs:

i5-2500k @4.3Ghz

560 Ti

8GB RAM

As redronn says, the game can run below min specs, though we can't make any guarantees. 

Trying things like updating to SP1 if you're on Windows 7 or reducing sound issues can help if the issue is related to your CPU. 

http://answers.ea.com/t5/Technical-Issues/Black-screen-at-startup-Troubleshooting/m-p/4855703#U4855703

If you're still out of luck you won't need a refund this early, you can just cancel the pre-order.