Playing with the numbers here:
http://web.mit.edu/lochie/www/erange/main.html
...shows it can be made to work, provided the thing has very low drag (I was using a battery specific energy of 200 for a LiPoly cell). Given it's a streamlined blob with stubby wings, that seems vaguely plausible.
Anyone with a better grasp of the principles want to comment?
Update: I found their tech page (see link upthread). They use lithium ion. They have about the same specific energy as lithium polymer.