Projection to handling overdue actions


I’m looking at using event sourcing in one of our products, and I was wondering if the following is something that can be done with a projection alone, as it feels like it might be.

Part of the system involves tasks that have to be completed within a certain time frame, on creation of a task the event associated with it has a due date, which is variable and user configurable so gets stored as a property on the event.

Would it be possible to set up a projection for a category that looks for any streams that have a TaskCreated event, but don’t have a corresponding TaskCompleted event prior to the DueDate that’s on the TaskCreated event? And then from that automatically create a “TaskOverdue” event?

At the moment we have a worker process that runs on a schedule that handles a number of situations like this so if we could use projections to automatically do this it would simplify a lot for us.