I have the same CPU, and I am running 2666MHz on my memory.
Wow, I'm jealous.
Would I be able to use high speed RAM with the Intel Stock Cooler?
Oh, and it turns out the memory standard of my motherboard is 1066/1333/1600.
I've found a Z87 motherboard for about £7 or $10 more. It can support up to 2400Mhz without overclocking and 3000Mhz with overclocking.
This is why I've decided to get 2400Mhz RAM.
The new Haswell chipset does not officially support 3000MHz memory modules. However the chipset which as you say is Intel Z87 is designed for auto overclocking. It is a kind of "turbo mode". There should be no issues using the stock cooler, since Z87 Haswell allows for independent overcloking like other chipsets. That means that you can overclock your memory without overclocking your CPU.