Ideally no, but then all sorts of things would be coming and going from your yard. Leaving a gap at the bottom keeps your fence from trapping soil and water and thus from rotting the fence bottom. And if you ask your termite control company, they will tell you this is the only sure way to keep termites out of the fence.
A way to have the best of both worlds is to use a CCA treated pine board at the bottom, most commonly a 2×6 and called anything from a base board to a “Kicker board”. This board allows the fence itself to be up off of the soil while the base board holds the soil and closes off the gap at the bottom of the fence. Termites tend to avoid the treated board. In most cases, even if the board does decay it can be replaced more easily than your fence.