Netlify continuous deployment is triggered by a Git commit, but you can run arbitrary Node scripts (though not _just_ Node scripts, of course) as part of your build process. I don't know of a way you could trigger deploys based on changes to the Google Sheets app without some code on your end (maybe IFTTT could work?), but everything else should be feasible if I'm understanding you correctly.
That's what I thought, I'll probably need another step somewhere that triggers the syncing and then pushes to git. After that Netlify CD would do the rest. Thanks.
I've setup that flow by adding a custom script in the google doc that triggers a Netlify build hook. You can tie custom scripts to an image (so you can make it a publish button).
