Definitely. Even outside of the animal proteins, shopping at farm markets and such is remarkably cheaper.
One of the main hurdles for some friends has been purchasing less than picturesque veg. I challenge them to find the ugliest ones (without bruising, etc), which does help the conversion :)
oh yeah! Not a farmers market. Those are $$$. Find a farm market where a lot of immigrants shop. They're typically smaller buildings with lots of stuff crammed in. Often the produce is stored on homemade wooden racks.
The one I go to is called Persian Market, but there are a few other Italian ones that are almost as good. Dig around Yelp for farm markets under a single dollar sign.