My understanding is NO (up to 1080P). Even though the 7950 or 7970 is a stronger card, however, Apple highly optimised the 5870 for FCPX / Motion. The result is that the 7950 only a little bit faster (in general) than the 5870, and the 5870 may be even faster on some particular task.
For 4K, I don't know, my dual 7950 setup works very well. But I didn't own a 5870, so can't compare.
The 7970 should be a better card (if you know how to power it).
If you can get a very cheap 7970, may be still worth to upgrade. But don't expect too much.