You can connect all 24 pins of the ATX 20+4 power connector from the power supply unit to the motherboard's 24-pin ATX power connector.
You still need to connect a 4-pin ATX power connector from the power supply unit to the motherboard's 4-pin ATX power connector. This is strictly a +12 Volt power connection and is used by the CPU's VRM circuit to provide power for the CPU. If left unconnected the PC won't boot because the CPU isn't receiving any power.
Corsair calls this connector an EPS/ATX12V CPU Cable connector that has 8 pins. This connector is actually made up of two 4-pin connectors. You will find that the connector can be split into two 4-pin ATX12V1 connectors. Just use one of those 4-pin connectors for the CPU power connector.