We have a 2005 Georgetown (bought used) and the dealer's service manager told me that everything you turn on using the dash switches works off of the start battery. And, it is not charged by the 30/50 amp shorepower. He also said the engine alternator trickle charges the house batteries and I have proven that to myself.
Remember that the start battery is a different animal from the coach batteries and does not bounce back from a full discharge very well.
The solar charger deal sounds like a good idea.
Life is a journey, not a destination.
2005 Georgetown 359ts
Bill & Virginia, Kentucky
Nights camped in 2011...78 , 2012...73,
Nights camped in 2013...123, 2014 ...101