In a word, no. The patronus must take the form of something that creates positive feelings (a dementor is by definition the embodimentsembodiment of unhappy feelings, primarily fear) and the shape of an animal with whom they share an affinity. Not only would someone who had an affinity for a dementor be unable to cartcreate a patronus, it's also fairly questionable whether a dementor qualifies as a 'animal':
"This ancient and mysterious charm conjures a magical guardian, a projection of all your most positive feelings. The Patronus Charm is difficult, and many witches and wizards are unable to produce a full, corporeal Patronus, a guardian which generally takes the shape of the animal with whom they share the deepest affinity" - Wonderbook : Book of Spells
and
"A Patronus is a kind of positive force, and for the wizard who can conjure one, it works something like a shield, with the Dementor feeding on it, rather than him. In order for it to work, you need to think of a memory. Not just any memory, a very happy memory, a very powerful memory… Allow it to fill you up... lose yourself in it... then speak the incantation " Expecto Patronum " HP:PoA (Film)