I might be wrong, but I'm pretty sure you can.
Looks like the brake is mounted from the bridge and I assume it works okay. There are no bosses in the pictures of the disc trucker so that would be the only option. I don't know whether it is advisable or not. I'd probably shy away from it myself, but that is my choice. Mounting a brake there on a bike that may not be designed for it may or may not void the warranty. I'd ask first if concerned about that. Surly has been know to be finicky about stuff like that. They have reportedly voided warranties for mounting kick stands that clamp on the frame tubes for example.
If the OP likes Surly bikes the Cross Check does sound like a decent fit for their needs. It is a do everything bike with rim brakes. I had kind of forgotten about it too.