The answer is absolutely yes.  The way the 1315 works is it first charges
the battery it is attached to, then, when that battery reaches the proper
level, the 1315 starts to also charge the other battery.  Result:  When
driving, the engine battery gets pulled up to snuff and then the aux battery
is charged.  If engine off and charger is attached to the aux battery, the
the reverse takes place.  How do I know?  First, the specs but mostly I have
the identical setup that you describe you are putting in and that's the way
it works.  I have a voltmeter mounted with a switch that can look at either
battery so I can see what is happening.  And my charger is hardwired into
the 110 and the aux battery.  Great when I have 'shore power', no switches
to worry about and all interior accessories are wired to the aux battery and
it stays up well over 13 volts.
BTW, don't skimp on the size of the charger.  Get a 25 to 30 amp 'smart'
charger, usually three stage, something like this (that I have):
http://www.progressivedyn.com/prod_details/rv_conv/rv_converter_pd9130_2.html
and with the Charge Wizard.  The small 'battery tenders' or 'maintainers'
are only good for just that, very small output and not enough to bring up a
discharged battery when in the field.  Only for 'tending' while parked in
the garage.  I tried one, didn't do the job at all.

On Feb 12, 2008 8:17 PM, Jeffrey Vickers <jeff@vickersdesign.com> wrote:

>
> Will the starter battery charge (through the 1315) if I wire the 120V
> charger to the aux battery? Or would it be better, because of the two
> types of batteries, to get a dual bank charger like this Schumacher
> and charge each battery independently?
>
>   <http://wwww.batterymart.com/p-schumacher-10-20-amp-charger.html>