The Davis have an offset presser bar, I don't think they would line up correctly, the National presser bar is about 1/8" closer to the needle bar than the White. I've tried some White attachments on a National, and not had them line up with the needle correctly. And with some, they were too "short" so they did not hold teh fabric firm against the feed dogs.
I love vintage attachments - it's the main reason I have such a variety of machines - so I can have a machine for each type of attachment set.