If the wiring and outlets check out to be in good safe condition, I see no reason not to reconnect the wiring to them. I would check the wiring over as carefully as possible (or replace the disconnected portions) as the main reason I can think of why someone would disconnect it is due to some damage to it somewhere.
I know that it's a lot easier to spend someone else's money, but at some point you would probably be well served to upgrade that converter to a modern one such as a Progressive Dynamics 92xx series (9245 or 9260 would probably be entirely sufficient). It would almost certainly charge the batteries faster when depleted and be gentler on them once charged and probably supply cleaner DC power to boot.
