It was a big deal a few weeks ago locally, Wendy's said they were going to start changing prices at different times of day. There was so much backlash that I believe the entire plan was scrapped.
After perusing this thread yesterday, I did some googling, and saw that both McDonalds and Wendys and possibly Burger King have experimented with this pricing scheme.
When I'm traveling I'd have no idea if I was being charged more than a store's regular price because I wouldn't know what their regular prices are, but locally I know the prices of the things I buy from the businesses I frequent.
I think there's a pretty good chunk of the population that wouldn't even notice. There seem to be so many that really don't pay attention, and I don't think the depth of their pockets is a factor, it's just a human trait for some, I think. The problem for the companies would be the chunk of people that will notice and who might get upset enough that they write that business off forever. It's not a good policy to try things that could lose you your best customers who frequently visit your business.