i wouldnt think,,that the problem is in the 4wd,that is draining the battery power,,sense it gets no power with the ignition off,,
after the battery is charged,,have them to load test it,,just to check the battery for sure,,it could have a dead cell and need replaced......also,load test the charging system after you install the battery with the engine
running,the alternator could be bad.........with a hot battery,the transfer case actuator may work,,,if not ,it will need to be replaced.....
to answer the question,,yes,you can unplug the actuator till you can afford to fix it,,just make sure you get it into 4hi first,,,,,cover the plug with tape to keep the dirt out..
again,i think your problem is in either the battery or the alternator here