It could be made to kinda work (with some extra coding on my end), but I don’t think it’s the right place for date based stuff. The issue is that the current styling is meant to style the “state” of the outline. Style only update when the outline state updates. But time isn’t part of the outline state, so there’s no way to cleanly/efficiently rerun the styles as time ticks forward.
I do think there’s a good solution to the general problem problem of “make this thing red when it’s overdue”. But it will require a script that periodically searches the outline for overdue items, and marks them as such. I don’t expect this in the next release, but maybe after that. I would likely add this at the same time that I did “Reminders.app Integration” as listed here: