Playing co-op is definitely possible in this situation. You are correct that the games will have to have the same patch/version number.
All Xbox 360 games, whether disc or downloaded, will update to the latest patch when the game is started and your console is connected to Xbox Live. The patch is stored on the hard drive, and will be installed whether you use the disc or downloaded version.
Therefore, you will need to connect to Xbox Live at least once to update. This should not be a problem if you are playing co-op over Xbox Live (the game will force you to update or sign out of Live), but playing via system link/network play will not automatically update.
If you are playing over system-link, be sure that both of you have started Portal 2 while connected to Xbox Live at least once recently. An Xbox Live Gold account is not required, the free account version should be sufficient for the update.