While going through a WP7.5 background transfer service policy, one can read the following:
The background transfer service does not run on non-simultaneous voice and data networks including the following: 2G, EDGE, Standard GPRS
So if a client's only connection to the internet is EDGE, my application won't be able to upload files with background transfer services at all?
Correct, unfortunately it is completely possible that BTS will not work for some of your users.
Consider using the network information APIs to warn users when they're not on WiFi or fast enough connections.
You could even try and get fancy, recording the network information every time the app starts up - and after a few consecutive EDGE-style connections, warn them.