Never tried it but it _should_ work with only the 8 pin one - at least at stock settings.
Once you are overclocking (which is the very reason this board exists) you need all connectors to provide stable current to the CPU.
If your PSU does not have the required connectors I suggest you get a new PSU instead of unintentionally frying your board, PSU or CPU altogether. 😉
Yeah I've overclocked on just the 8 pin, I was just wondering why the 4 pin exists too and whether it would fry the board if I connected the two.
I've also got the Corsair HX1000i so should be fine.
You can connect both the 8 pin and 4 pin cpu power cables, it won't hurt anything.
The 4 pin is for extreme overclocking.