Howdy Duncan,
Yes, there are people who use scaled up card model plans for flying aircraft. Some use a balsa framework and others use foam as seen on this link
http://www.fiddlersgreen.net/fgmodel.../motorized.htm stop by and look at the pics.
Alot of the card model planes are designed to fly, like all of the free models offered here:
http://homepage2.nifty.com/ojimak/interest.htm
stop by that site and download any of the models in yellow, click on the name for the model parts file and click on the picture for the instruction file.
I have a friend who makes card model rockets that fly using estees type engines, including several versions of the scud missile and others at:
http://www.geocities.com/coldwarriorcards/ and as always, all the models are free.
Have a good day,
Greg aka GW