It will work just fine with no load whatsoever in the trailer. Suspension and axles work together to absorb weight and road bumps/dips. Don't let the bowed axles bother you, unless the bow is downward...
Welcome to the forum.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired