Likely not impossible, but the crucial weak point would probably be the connection with the seat tube. Independent of the material, that place would need some heavy gusseting/reinforcement. That particular bike also has a very vulnerable connection to the head tube, as only the down tube connects to it.
There are bikes without a rear triangle, but they (almost?) always lack the seatstay instead of the chainstay or have what could be considered something in between a chainstay/seatstay. Here are some examples:
There are bikes without a rear triangle, but they (almost?) always lack the seatstay instead of the chainstay or have what could be considered something in between a chainstay/seatstay. Here are some examples:
http://i.imgur.com/F1xkdc1.jpg
http://i.imgur.com/oTFbEy7.jpg
http://i.imgur.com/XxRNe5y.jpg