I spent some time corresponding with Glowforge back before the order deadline and asked a lot of questions. You cannot print directly from your own computer, nor directly from CorelDraw or any other software you own. The thing I found most concerning was the software they operate on the cloud, taking your file and therefore "sharing" it with the universe. Here is one of the responses I got, which I felt was a bit vague:
Dan Shapiro (Glowforge)
Sep 29, 20:01
Jumping in for Jason, who is out at the moment - You keep your original files on your computer, then send a copy to the Glowforge server which prepares them and sends them to the machine.
The software that actually runs Glowforge runs in servers that we operate, so you don't need to install anything (other than your drawing software like Coreldraw). You access it from a web browser.
It can handle compound vector/bitmap files no problem.
It has pretty much everything we've seen in all of the leading lasers' control software, and a great deal more!
The internet is required to use the Glowforge. Most print jobs fit in the Glowforge's local print queue, so you just need the connection to start the print. If you lose connectivity while printing it will finish. However, bigger jobs may not fit and are sent down in smaller pieces. If you lose connectivity during a big print it will finish what it was doing, pause, and wait for connectivity to resume.