No. The SSPI port can only configure the LatticeXP2 flash or read from the LatticeXP2 SRAM. The SSPI port can not write to the LatticeXP2 SRAM.
The SRAM can be configured using JTAG, the external Master SPI port, or by using the data stored in on-chip Flash. If you want to configure the SRAM you will need to use the JTAG port.
Please see the SSPI programming technote for the LatticeXP2 product on the first page, under "Programming Overview".