Many PICs have the same, or very similar RTCC,
but very few have a Vbat circuit at all.
Of those devices that have Vbat, quite a few have serious Errata about Vbat operation.
I would initially suspect that Vbat will power the secondary crystal oscillator and RTCC internal registers,
and nothing else, when there is no Vdd available.
For PIC32MK__GP/MC Family, Datasheet have this:
RTCC Pin Output — Real-Time Clock Alarm/Seconds Output (not in VBAT power domain, requires VDD.
But for that device family, there are other errata about Vbat.
But why at all do you want to shut down power to PIC Vdd when there is power available for other external hardware to work?
The normal way to do what you want on a PIC microcontroller, would be to set PMD register bits for all peripherals that are not needed, set all I/O pins that are not used to output Low, set all outputs that are used such that they do not feed power out, unless you clearly want.
Then make the PIC go into Sleep mode.
You may then get PIC to wake up from RTCC interrupt, from Timer 1 interrupt, or from some other signals from outside.