It depends. If just going for a few things, then no I wouldn't. But if I'm planning a big stock up trip and know I'll already be spending a lot on the food, then yes I will drive further to get more for my money.
It would depend on how much I was planning to buy. If I were just going to pick up..say, bread and milk, then no. If I were planning to stock up, then yes, I might drive the extra distance for better deals.
I travel 20 minutes to whole foods sometimes because I don't like our market here. It's overpriced for what it carries, and the employees need better training. It's cheaper to go to whole foods as far as price is concerned, but almost evens out since I take the ferry when I go. I'm going to try another grocery store about 20 minutes away this weekend, but it's on the island. I will travel if the store is better I don't mind paying more even as long as the quality of what I get for that price is worth the extra effort.