It won't hurt, but, IMHO, it won't help, either... I would get the tires off of the dirt for long term storage (over-winter), but, there is sufficient space for air circulation between the ground and the bottom of the trailer to keep that air space at the ambient humidity...nothing to be gained in the storage scenario for trying to block the ground effect on the humidity, particularly if it is only under your trailer and not the surrounding area.
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)