Hi,
The problem is that what you're describing is the opposite of what most people want to do, i.e., turn it OFF when the user starts Outlook. I mean, there not out of office, they've just logged in!
I'm not aware of a way to do this in Outlook. There may be a way in Exchange, I'm not sure.
I think if it were me, I would continue to disable access via GPO, turn off the OOF (to prevent any more prompts), then set replies that come from outside the company to automatically respond with an OOF-type response (either through rules or custom programming). Just my two cents.