I'm not sure if you can link both projects, however, I think Apps script email service would still be limited by it's own quotas.
A possible workaround would be to call the Gmail API directly instead of using the Apps script Gmailapp service.
To call the API you can use the "UrlFetchApp.fetch()" to make the call to the Gmail send endpoint.
To be able to make the call to the Gmail API, you will have to enable it in the developer console, for this in your script go to "Resources -> Advanced Google Services". There you will enable the Gmail API, then you have to click on the link that says "These services must also be enabled in the Google Developers Console."
It will take you to the Developer Console of your Appscript project, there you also have to enable the Gmail API.
The quota for UrlFetch is 20k calls/day, so in this case you would be limited by this quota and the Gmail API quota.