Yes, when you subscribe to a Campaign, the responses will be seen in your "Needs Attention" tab.
If another agent responds to that message, that conversation will no longer be in your "Needs Attention" tab and will be removed from your inbox.
If you, as an agent, respond to that message, that conversation will move from your "Needs Attention" tab to your "Participating" tab.
If you miss the initial response on a message, but the end user responds, that conversation will appear on the "Needs Attention' tab.