Yes, they will! We only make temporary copies of the files onto our servers. Like a big old Xerox machine from the future!
The copies we create are scrubbed after seven days, so don't delete the files from your hard disk or device if you want to keep them around for a bit longer!
This also applies to files handled by our app, Collect - we make copies of your files, we don't use the originals, so even if your boards expire, you should still be able to access the file if you've got the original saved on your device.