When one adds a liquid to another liquid, there'll be an energy to dissolve it and it is called free energy of solution. Theoretically, if the added liquid is taken out of the solution, exactly the same amount of energy is required.

So the answer to your question is, DEE still evaporate but to a lesser extent depending on the free energy of solution. But evaporation of DEE from biodiesel is unavoidable.

yes, DEE will evaporate but you can reduce using fumigation process