Yup, the control board runs on 12V. No 12V, no workee.
With the newer rigs (yours especially), Montana is using a intelligent converter with multi-stage technology. This means it won't cook your batteries as older converters would do. So leave the converter on all the time. It won't hurt anything.
Inteli-Power 4500 Series models can recharge the battery to 90% in 2-3 hours using our patented Charge Wizard technology.
The built-in Charge Wizard automatically selects one of three operating modes: BOOST, NORMAL, STORAGE.
BOOST Mode - Indicated by green LED remaining on. The output voltage is 14.4VDC to rapidly recharge the battery up to 90% of full charge.
NORMAL Mode - When the battery is between 50% and 90% charged, the green LED will flash once per second. When the battery has reached 90% of full charge the green LED will flash 2 - 3 times per second. In this mode the output voltage is 13.6VDC and the converter is safely completing the charge of the battery.
STORAGE Mode - Indicated by green LED flashing every 6 - 8 seconds. In this mode the output voltage has ben lowered to 13.2VDC, the RV battery is fully charged and the converter is maintaining the charge.
http://www.progressivedyn.com/all_in_one_pd4500_1.html