Honestly a full stomach and an empty stomach just controls how long it takes for the DXM to kick in. An empty stomach for me takes about 45 minutes to an hour to kick in, whereas a full stomach can take up to 2 hours to kick in. Then you have to wait for the peak.
IMO, it's best to do it on a light or empty stomach for the best experience. Not to mention DXM can cause nausea/vomiting (it sure has for me, just DXM alone) and eating will probably increase that feeling.
If you want to hear a brief experience...
I had a friend try DXM for the first time, he was really hungry though. After downing 10 Robo-gels, he decided to make a sandwich. Five minutes later he was dry heaving in the bathroom. It took him about an hour to throw up the sandwich, then he layed on my couch and was convinced he was dying. Needless to say, he had a great time after this. Can't really PROVE it was the sandwich that caused the nausea, but it was a low dose of DXM, so.
Eat lightly or don't eat until you're tripping