eFUSE is not supported on Xilinx Series 6 Evaluation Boards (SP601, SP605, ML605) due to the fact that the development boards were not built with an on-board embedded version of the USBII download cable circuit.
The USBII circuit is a requirement for eFUSE as per the iMPACT documentation (iMPACT Help - Introduction to eFUSE Registers).
The Series 6 development boards can only be programmed via the onboard download circuit as there is no provision for the use of an external download cable connection into the board's JTAG chain.