It's possible. For it to work like you want, the custom calculate script in the Today field should be:
// Custom calculation script
(function () {
// Get a reference to the DueDate field
var f = getField("DueDate");
if (event.source && event.source === f) {
// Don't proceed with this script if triggered by a change in the DueDate field
return;
}
// Update this field's value to display today's date
var d = new Date();
event.value = util.printd("mm/dd/yyyy", d);
// Add seven days to today's date
d.setDate(d.getDate() + 7);
// Update the DueDate field
f.value = util.printd("mm/dd/yyyy", d);
})();
But first remove the calculation script from the DueDate field. If you don't make the DueDate field read-only, a user will be able to change it, but it will get reset when any other field value is changed.