Sounds like an opportunity. Gather posts by executives and add to an activity stream with other relevant data available to the public?

There's probably no technical barrier preventing it, but I can almost guarantee that it would violate Facebook's terms of service. They're decidedly unfriendly to bots.

And Data Protection issues in some places.

How are you supposed to know this link if you have no facebook account? It's not on the company page, it's nowhere available unless someone either sends it to you directly or you have a facebook account.