The specifications of the Vapor X 7970 Ghz Edition indicates that it takes 2.5x slot. That means crossfiring would take 5 slots in total. The card itself is 5.2 cm. That's not that big, while the V Pro is quite generous in size.
It would fit. But the only problem would be that you are covering the other PCI Express slots. Other than that, yes, it should fit.
Of course, if you are ever in doubt, you could either:
1. Purchase a smaller 7970
2. Buy it anyway, and return it if it does not fit.
These may not be convenient, but they are options if you are ever i doubt.
IMO, they should fit.
As always, please consider selecting my answer as the solution if it has helped. Thanks