If the MAX32650's 120Mhz oscillator is enabled (when the main clock source is the external clock, PCLK is based on SYSCLK) can I still run the SDIO controller without switching SYSCLK?

Yes.  The SDHC runs from the high frequency internal oscillator divided by 2. This is independent of the selected system clock. Note that the high frequency internal oscillator must be enabled for the SDHC to communicate.