The fan cools the converter. If you're not on 120VAC, the converter isn't doing anything, and therefore doesn't need cooling and the fan won't run. If you've drained the battery and then plug into 120VAC, the converter now has to recharge the battery. The fan will now run if necessary. If you're on 120VAC and running a substantial 12VDC load, the fan may run, also.
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10