Normally it can't. The normal boost output feedback pin FBS is set to 0.5V, but the threshold is 0.56V if we want MAX38888 to charge to the SuperCAP.
So if the system conect 5V to the VSYS pin, and want it to charge to the SuperCAP, the VSYSmin can only be set to about 4.4V.
So when the system is powered down, the boosted output voltage can only be about 4.4V.