Yes, the motherboard needs the 12v to function.  By disconnecting the battery the motherboard turns off which will not allow the ignitor the ability to turn propane on if it calls for it. 

Don't worry about a few parasitic draws, they are minimal at best and as long as your battery is in decent condition you don't have to worry about a dead battery after only 4 hours. 

We don't disconnect our ground cable off the battery (no battery disconnect) unless it is not being used for 5 days or more.  Even then with a fully charged battery 'at rest' you should read 12.72v or better and after 4 days our battery will read 12.61 to 12.64v (we have a pair of 12 v).  Just don't run it below 60% S.O.C. or 12.2v for maximum longevity.  We more often then not boondock and our batteries give us great service even though they are well over 10 years old.