Yes, any Manuscript app on any device can read .manuscript files.

Just export a ".manuscript" file from iPad or iPhone to Dropbox or email (under export choose the .manuscript full backup option). Then simply open that file with the Mac version.

Manuscript for iOS is able also to import .manuscript files.

The best way to work with both platforms is to have Dropbox account and save your results in Dropbox folder on Mac. When you need to continue your work on iOS device, just import your manuscript from Dropbox. After you finish - export it back.

Thanks to Dropbox, this file automatically updates on your Mac and you can go on your computer.