Yes, you normally configure SPI with SPE being zero. The clock for SPI as a module comes from RCC so it has to be enabled there, but it probably is all the time.
SPE enables SPI's internal state machine, i.e. it starts to transmit, receive etc. At SPE down the internal counters are reset. If you change e.g. CPOL/CPHA or number of bits while SPE is not clear, the results may be surprising (guess how do I know).
JW