In reply to Indy:
Not quite what you asked for but...
Save the GPX or TCX file to your computer.
Plug the Edge 800/810 in to your computer. Once connected, it is recognized as a USB drive.
Open the "Garmin" folder in that drive.
Find the folder labeled, "NewFiles". Move your downloaded TCX or GPX file there.
Once the file has transferred, you can disconnect your Garmin.
Now turn on your Garmin 800/810. The route should be available in Courses on the device.