Probably not, unless there is a BIOS setting that controls power to the USB ports. It will depend on your board. Some boards provide power to the USB ports with the system off. Also, check the Intel product guide, for your board, +5 V Standby Power Indicator. There may be a description of where 5 V standby power is availble on the board with the system off. For the DX58SO, standby power is available at the memory slots and the PCI bus connectors.
Check the product technical manual for the DX58SO2.