As with all things there are pros and cons though most of the pros aren't really relevant if the web site is designed correctly and the end user has a fast Internet connection. So the relevance of these depends on your target audience.
- The base level images arrives quickly thus ensuring the layout is correct as soon as possible. However if the height and width attributes of the image are set correctly this is pretty much irrelevant (thanks @DA01)
- It's clearer that the page is still loading if images are interlaced when loading on a slow internet connection.
- It can be worse seeing a blurred image than no image at all. You wait to see if the image is important, whereas if there was no image at all you might not be bothered.
- As others have mentioned in their answer, interlacing increases the size of the image files thus increasing the load time of your web page. This gives a worse experience for everyone even those on a fast connection.
So on balance I'd say it'sit probably doesn't give a better user experience.