This one suggests it depends on the consumer, with "highly numerate" consumers being less likely to think the price is lower (but presumably also less common in the customer pool):
Edit: searching for "charm pricing" specifically suggests it does work, but I suppose maybe there's some bias on the context in which people use that term.
My point is getting the consumer to eat the sales tax on top is just a wise trick by US businesses, and nothing to do with complexity.