That's a very sensible question, let me take a stab at answering it.

So, for 99% of things, it's all stored on Google's servers. ActiveInbox is a lot of UI enhancements to create a new way of controlling your email, but it does it all with a clever use of Gmail's labels.

The only thing that relies upon the server is if you're a Plus user (including the free trial), to store your preferences on our server; and to store 'Conversation Notes' (a text box at the top of all conversations for planning next actions, a quick memo of what the entire thread is about, and links to related information if needed).

We are trying to figure out a way to do Conversation Notes purely with IMAP, but we haven't got a really fast/reliable idea yet, so we're sticking with our own servers.

But yes - for everything that is important to your organization, it's all labels.