I wouldn't be doing that myself!!!!
To put a drop of oil onto your card, back or front, you would find absorbed into the paper leaving a definite mark where you put it. With time it would most probably work through to the image and spoil that. And then if you're gonna put on the drop of oil on one card and immediately shuffle through your pack, well...multiply the damaged cards by 78, 80 if you keep in the extra two however they might be presented when you shuffle.
I also think the oil would make shuffling difficult anyway, viscosity and slowing things down by sticking them together. I don't reckon you'd get the extra slip you'd be hoping for.
Don't believe me? Get a deck of playing cards, the laminate is similar to most new tarot decks and try it. You should see some of the effect pretty much straight away, but let it sit and watch how the oil gets into it with more time.
If you really wanted to use a scented oil, essential or fragrant, maybe a piece of blotting paper or paper towel with a few drops on it, and then that placed in between the pages of the LWB. The fragrance should permeate all the contents of the box with time without damaging your deck with nasty oily spots.
If you have to put something in the box with the cards, I'd suggest perhaps a bay leaf. You'll get a mild herbal scent with the benefit that a bay leaf will ward off silverfish; bay leaves are usually nice and flat so one will slip in a box with its cards fairly easily; it will surely crumble with time but shouldn't cause any damage or marking to your cards being that it's nice and dry; and when it does crumble to nothing you can just go to your kitchen herbs and get a replacement.
