Generally, batteries like to be charged.
You should not let them go down to ~75% discharged (~11.8volts or 12.1 volts... I don't know the numbers)... because that will shorten their life.
We don't get a lot of sun in the winter, so we run our generator almost daily (we only have 2 panels) to charge the batteries to 100% (12.8 volts).
"things" will work as long as the batteries have the power... of course, they will also be depleted faster.
Here's a good article... somewhat related (my DH knows the author): http://sustainablepreparedness.com/index.php/blog/fine-tuning-battery-charge-settings