Assuming we have the same filter media, it's a paper filter. So no, you wouldn't add any oil.
The stock filter on these (mine anyway) isn't cleanable/washable/reusable. So if yours is dirty, you'll need to replace it outright.
It shouldn't need replacing very often either - it's pretty protected form the elements inside that box. This is a gross assumption but I wouldn't be surprised if you could go 20k+ miles on the original. I check mine every 1k miles just to be safe.