No, you can not register the GOG version on Steam. Some people have both versions from the kickstarter, though.
You can play co-op between the GOG and Steam versions, though. One thing to note, however, is that Steam appears to have gotten rid of the option to disable automatic updates. There is a delay of a day, or so, when Steam updates before GOG releases the corresponding patch, so there may be times you would not be able to play until the version numbers match again. That will be less of an issue once the patching frequency slows down, and may be eliminated if GOG Galaxy allows developers to update directly (don't know if that will be possible; GOG has always done their own game and patch installers).