How long is a piece of string?
It all depends on how discharged the battery is and what rate charger you are connecting up to re-charge it.
Regarding the second part of your question about needing a battery when connected to a mains hook up is debatable as some say you do and some say not.
Have a look at this thread for example.
A day of all things motorhome and campervan. The show is held both in the main indoor arena and across the grounds. Catering, hot drinks and food options are available. Easy access to the site and free parking included. Win one of five pairs of day tickets