You are also powering your CO detector and depending on your converter you may also be powering your television set (instant on comes at a price...your set is still drawing power despited being off), the same applies to your stereo if the front panel is lit. There should be a battery disconnect on your unit that will effectively isolate the battery from the TT. Unless you are connected to shore power (I'm fortunate that I keep my TT at my home and have RV hookups), whenever you are storing your trailer you should use the battery disconnect to prevent the battery from providing juice to the converter and 12v devices.
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)