If you look at my posted videos and other folks you will see not only is it possible but a lot of folks recommend it. Dr. Tim is one who comes to mind.
I've got ghost shrimp and some cherry in my all live plant tank. They eat stray food and algae. I really like having them around and I have about 8 Ghost Shrimp in my tank with a few pushing over an inch in length not counting their feelers.
Here is my current video: http://fishtanktv.ning.com/video/dwarf-baby-tear-new-plants
Look at about 2:30. I can post a better video of them. They come out in droves when I put food out.