I'm not sure a physical copy actually has to exist anymore, with the Check21 regulation a digitized copy containing the relevant information is considered to be the same thing as a physical check. I don't think there's anything in the regulation that would prohibit a consumer from creating the digitized version themselves. Now getting a bank to accept it from an untrusted source (a customer) as opposed from another bank might be hard.
Hm... this isn't very scientific, but I've read through a bunch of Wikipedia articles on the topic and nothing says explicitly this will be possible. Everything appears to be written under the assumption that a physical check exists to begin the process, and the article on substitute checks [2] explicitly refers to a "digital reproduction of an original paper check." Maybe someone who knows the actual regulation can chime in.