Yes, MachXO3 can be re-configured through SSPI/I2C/JTAG (sysCONFIG ports) by an external processor even after NVCM is pre-programmed. But make sure the NVCM is pre-programmed with the required sysCONFIG ports enabled in the Diamond Spreadsheet to access the programming ports.
Also note that, if the device is power-cycled, or a REFRESH command is received, or the PROGRAMN pin is asserted and released, the device will again re-configure the outdated configuration data from the NVCM.