I'm not sure if this is possible, but what I would like to have is a list of tasks such that the first thing in the list is the thing that is due first. Things that do you have an explicit due date should be listed at the bottom of the list, below the thing with the most distant due date. In the normal ascending order, things without a due date are displayed first, followed by the thing with the closest due date.
What you can do is select the records with no due date and drag them to the bottom. They will stay at the bottom, but they will get "today's" date. Hence they will appear last.