Implementing this is possible but not straightforward. I envision three approaches, all utilizing the Coda RESTful API. The idea is to use the addPermission function from the Coda API to add a new permission to a specific document.
Build an External App: You can create an external application that reads data from a Google Sheet and then calls the Coda API function to add a new user.
Use Google Sheets Pack + Custom Pack + Automation: With the Google Sheets for Coda pack, you can sync a Google Sheet to a Coda table. From there, you can build a custom pack that executes the Coda API function. As a reference, you can use the Add Page pack by @Paul_Danyliuk, which utilizes the API to add a page. You would just need to modify the endpoint to run the addPermission function, and of course, adapt the code with the correct parameters and results. Once your custom pack is ready, you’ll need to set up automations: one to update the synced table (daily, hourly, etc.) and another to trigger the custom pack formula when a new email is added to the table.
Build a Comprehensive Custom Pack: Another option is to build a custom pack that incorporates all the necessary operations, including syncing with Google Sheets, reading the data, and executing the addPermission function. This approach would streamline the process by consolidating everything into a single pack, making it easier to manage and automate, but you’ll need to manage authorizations on both the Google and Coda sides.
In summary, it is possible, but not very easy. You will have to do some Javascript work to make it happen.