Yes, you can. They should work at 1600 MHz.
You can install as much as 32 GiB of memory and it will work at 1333 MHz:
Do not blindly trust rumours which claim that you should be able to overclock the memory, always test your setup using the Stressful Application Test:
You can download it and build it on probably any recent Linux distribution, many binary ones offer pre-built packages of the Stressful Application Test and there are even some live distributions that feature it.
I use 32 GiB of some low-profile Netlist-branded PC3-12800E memory with Hynix chips (I think that it is this one: NVD1G7235107H-D12THM), 4 sticks of 8 GiB each, with a fairly recent AMD FX-8370. Event though the BIOS automatically set the frequency to 1600 MHz, I found it necessary to lower it to 1333 MHz manually (by setting the multiplier to 6.66x, down from 8x), otherwise the Stressful Application Test would lock up my computer after a few minutes.
Thus, although it is a fairly recent CPUâ€”one that was bundled with a Wraith coolerâ€”it still does not support memory speeds beyond the original specification.
Besides, this motherboard tends to overvolt the CPU, or at least mine does (using BIOS version FEf). Try lowering the CPU core voltage to the base frequency VID, 1.325 V, while you are at it, and test it. The motherboard board sets it needlessly high.