Depending on the equipment of your trailer, a battery will discharge overtime if the AC is not plugged in. Most appliances, hotwater tank, refrigerator, propane detectors and so forth draw a small amount of current from the battery. Overtime this ads up and will discharge the battery. DC lights will decidedly speed up the process and are true current hogs.
RV refrigerators work by heating the cooling gas. They can heat the gas three seperate ways – using propane, 110 VAC or 12 VDC. Most use just 110 VAC or Propane. 12VDC run refrigerators are rare because they use a lot of current. However all refrigerators when “On” draw current from the battery for the refridge controller board.
You did not mention if the propane was on when you parked. If the propane was off certainly no damagewas done to the refrigerator. If you're concerned you should plug the rig in and check. As well you should plug it in to recharge the battery. Batteries should not be left discharged.
When we park ours for any extended period over the summer we do shut off the water and propane but leave it plugged into electricity. This insures the battery is fully charged. Though we do not use our trailer much in the summer I'm always out there working on this or that.
Though we don't have a traditional RV Refrigerator we generally keep our trailer relatively level at all times.
Hope I did a better job this time and always glad to help out.
Norm and Ginny Milliard
1982 Sunline 15.5 SB
2004 Honda CRV 4 cyl, manual