@andrea scott there's nothing natively that gives you access to your team's notifications, however I created a product that, in addition to integrating Trello with Gmail, aggregates card mentions and card adds into a single inbox:
https://trello.com/integrations/#benkoboard
It also unwatches cards you're added to, so you only get notified about being added, mentioned and removed which dramatically reduces the noise to signal ratio.
You could then view your team's boards to get a view of which notifications they had dealt with and what their priorities were.
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