Most likely not by using the Migration Assistant. If all you want is your data, then simplest is to create an admin account on the old machine using the same credentials as what's on the new one, then drag & drop stuff from the new to the old. Do note that anything dealing with Mail, iTunes, iPhoto, and Safari most likely won't work. That's the stuff in /username/Music and Pictires. and in /username/Library/Mail and Safari.
27" i7 iMac SL, Lion, OS X Mountain Lion (10.8.5), G4 450 MP w/Leopard, 9.2.2
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