Yes, MoBL dual ports can be powered down.
Low power consumption and small footprint are the key factors on which the MoBL is based. It has an automatic power down feature, controlled by deactivating the chip enable (/CEL and /CER) and it permits the circuitry of each port to enter a very low standby power mode. The low power standby mode can also be achieved when both the byte select pins (/UB and /LB) are inactive, irrespective of the mode of /CE. During power down the output pin states are in the Hi-Z mode. The typical and maximum values of current for the low power mode (Isb3) are 2mA - 6mA for 1.8V, 4mA - 6mA for 2.5V, 6mA - 8mA for 3.0V I/O devices.
The condition for minimum power configuration is when both chip enables, both semaphores /SEML, /SEMR and the special function enable pin /SFEN are deactivated. Under these conditions, if the input I/Os do not toggle (f=0) , the power consumed is minimum and the current drawn will not be greater than that stated in the Isb3 specification for the device.
Each of the ports could be individually powered down.
The time taken by the MoBL a dual port to power down is specified in datasheet, i.e., from chip enable de-assert to the point when the operating current reaches the specified Isb value.