I like how Todoist does this. So when I receive an email in my gmail account, the email could be about something that I have to do or follow up on in the future. Todoist has an extension for Gmail where any email can be added as a Task where the email subject by default is the name of the task. You can always edit the name of the task though. The email is then listed as a task in Todoist and when I click on that task it could take me directly to the email.
This is very helpful because it makes clearing your gmail very easy. You can archive your emails knowing that it will not be forgotten and a date is associated with that email.
I think it should be possible to link to cloud based mail like gmail (or microsoft). When i attach my gmail to Todo there could be several options. The simplest way is that i can browse through my mail and the header, content and attachments of the mail that is select is copied to fields in the task that i'm creating or editing.
In this way it also could be possible to download all mail from the inbox and then in Todo i can create a task from each mail.
Interesting idea. Can you add some detail as to how you see the flow working? In other words, how do you imagine "linking" the email to Todo. When the task does come up due, what do you imagine is possible with the task.
I like this idea too. You can do it with their cloud service, but they talk about not being tied into a service so you should be able to do it without their service too.