A great deal depends on the type of charger. In Britain there are the old-fashioned ones that keep dishing out a charging current regardless of the state of charge the battery has reached. These will charge a totally flat battery but must not be left on permanently, as they will "cook" the battery.
The more modern sort is a "smart" charger, which has nothing to do with Ashcroft but is a charger that senses the state of the battery and stops charging when the battery is full. If you leave it on permanently this sort of charger just adds a slight "trickle charge" from time to time, and in fact it's recommended that they ARE left on all the time. These will not however charge a totally flat battery, as they depend on electrical feedback from the battery and a flat battery can't give that.
In theory there could be a yet more modern type of charger that would do both, but I've never heard of it. Maybe someone technical can add something here?
So, if your charger will charge a totally flat battery it's almost certainly unwise to leave it on permanently. Probably the best thing to do is to read the manual that came with the charger, or look up the manufacturer and contact them.