It sounds as if you and Bunsen are referring to the same animal by differing binomial nomenclature. If the AC adapter (to throw in another appellation) can power the PB in the absence of a battery, you have little concern about its aptitude. It would take a wide departure of your AC mains voltage (120VAC?) from its mean to have much effect on the DC out from the adapter (24VDC).

You will not have had time for the soak approach to rechargeing the internal backup battery yet, but I suggest that it is worth the time, even in the absence of the battery, to leave the PB attached to the active AC adapter for that purpose.

de