The Asus A88XM-E has a 2400MHz MEMCLK divider, so there should be no problems running HyperX 2400.
It's only a 3+2 Phase board without a VRM heatsink, but the GeminII M4 should take care of that, especially with the option to fit a 25mm thick fan on it instead of the 15mm one it comes with.
I would almost be tempted to suggest going with the A10-7870K instead of the 7850K since its around the same price and comes with a much better cooler.
The 7870K heatsink is fairly close in design to the GeminII M4 as they both have 4 copper heat pipes while the 7870K cooler has more depth and a copper baseplate the M4 covers a wider area by about 40mm.
If you made do with the 7870K cooler instead of the GeminII M4 you could replace its 70mm fan with anything up to 120mm and have, maybe, enough saved to get a Seasonic M12 PSU. With less overlap on the CPU heatsink you could probably rig a VRM heatsink later on (using the CPU mounting screws) if it was necessary.