Hi bob,
0.5 volts may be a 5% loss. Many inverters "alarm" at 10.5 volts. According to Wagan yours does, so yes if you wish to run the fan on high you need the direct to battery connection.
http://wagan.com/wagan-tech/power-inverters/elite-200w-pro.html

Oasisbob wrote:
Thanks for the great advice. Much apreciated and will file for in case the battery direct cord the manugacturere promised me does not work.I am skeptical as I only lost half a volt going through the trailer plug versus straight from the battery according to my electric tester. We shall see