Because of the rationing, vans selling ice cream became defunct. However, because of the refrigerants in an ice cream van they were in some instances used to carry blood for blood transfusions to the soldiers needing medical attention.
It is possible that an ice cream van would have been used during the war for this purpose, but as for any factual evidence of one being used for the D-day landings I think you might be hard-pressed to find anything as it wouldn't have been considered that unusual.