I'd say you might want to CAREFULLY experiment -- as in, "with all due fire safety precautions in place along with a few extra precautions in a flame-proof area." An incense stick *might* act like a wick for the oil, although I'm pretty sure the scent would be affected. Other possibilities that come to mind are an uncontrollable flame, the stink of burning oil, or the oil dissolving the incense stick.
Now that I've written that... I'd suggest just buying more incense sticks. It's probably a lot safer! 😁
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