Clearance appears to be 265mm, or 10.4".
So, NO, the card does not fit as it is 10.5".
I don't however recommend a GTX770 4GB card now that the GTX970 and GTX980 cards are coming.
The GTX970 for example is likely to be roughly the same price ($400) at a higher performance. We should have more details TOMORROW at the NVidia event.
It's uncertain if the GTX970 will be a 3GB or 4GB model but IMO as long as you have 3GB there should be nothing to worry about but if the price difference was minor I'd get a 4GB model.
I should add it's likely the new GTX970 will be much QUIETER with a half decent cooler based on how much more efficient the 1st generation of the Maxwell GPU was with the GTX750Ti than the current Kepler architecture.