That is possible, however I doubt the processor can underclock to a low enough power so your standby time would be in the region of hours/days at most. I've not yet examined the hardware thoroughly enough to be certain though.
EDIT: OK it seems I was wrong, all the required hardware seems to be there.
jz4740 datasheet wrote:― Supports six low-power modes and function: NORMAL mode; DOZE mode; IDLE mode;
SLEEP mode; HIBERNATE mode; and MODULE-STOP function.
jz4740 datasheet wrote:RTC (Real Time Clock)
― 32-bit second counter
― 1Hz from 32768hz
― Alarm interrupt
― Independent power
― A 32-bits scratch register used to indicate whether power down happens for RTC power
jz4740 datasheet wrote:Watchdog timer
― 16-bit counter in RTC clock with 1, 4, 16, 64, 256 and 1024 clock dividing selected
― Generate power-on reset
Dingoo must have some really shit lazy programmers if they couldn't even be bothered to implement time/date, but then if you look at some of the sdk code and makefiles then that's pretty obvious.