GTX 470 Gigabyte

Will GTX 470 be able to run BF3 in full HD in combination of i5 3450 and 32 GB ram?

Also will I have hit problems...?

I had no problems to play BF3 on 1920x1080 high details on GTX470 and later GTX480. CPU shouldn't make big difference in minimum FPS. In worst case you will have to lower details to medium or something.

You should be alright with a 470, it has 1280mgs of ram which makes a good difference over the middle of the line current 560 1g runs. It is basically a 560ti 448 core with a lower reference core, though the 470 has a lot of headroom to overclock. Should be a good card for medium and some high settings in BF3.