Yes this should be possible. I haven't done dates but I have windows where I copy the Title, Description, Catalogue Hierarchy from the Request window on to the Request Task window using runtime values.
So when I select the Add Task action in the process designer in my Request process and the task window appears , I rightclick on the field, select "Value Type" then "Specify a runtime value for control" and browse to Request/Catalogue Hierarchy Cateegory to pull through the info onto the task window
You could try to create a new Date/Time attribute and do a calculation set to "After Read" that will populate the new attribute with data from the other. Calculations are still soft of new to me but I do use this for copying RaiseUser/Title from an Incident window to an Incident Task window. We also use it for our HR stuff.