No, do not leave the unit connected 24/7 with the supplied "charger"; it's nothing but an unregulated power supply which has no way to determine proper end of charge, nor will it reduce the voltage to a proper float level. In fact, as the battery becomes charged and accepts less and less current (Amps), the voltage will rise to damaging levels. I've measured 2 of these bricks outputting over 17V. Even at a few mA, given enough time, the supplied wall wart will "equalize" the battery to death if left connected.
If you do intend to use the supplied "charger", get yourself a multimeter and monitor the voltage throughout the charging process and terminate when it reaches ~14.4-14.7V (official specs for the enclosed PowerSonic 33Ah battery). Then disconnect and store for 3 months and check it again. Better yet, use a proper 3 step smart charger that has bulk, absorption and float stages.
BTW, the reason I keep putting "charger" in quotes is because the supplied brick is not really a charger, it's a power supply which really should not be included with this unit at all.
answered 1 year, 6 months ago
No, this is fine.
answered 1 year, 9 months ago