If I send out an email (manually or via an automated followup) does CM automatically consult the Suppression List so that it does not send to that email?
And if someone resubscribes or is added via the API, will that remove that email from the Suppression List?
It depends :) By default, a subscriber will automatically be removed from a list once they are added to the Suppression List. Assuming they had been added to the Suppression List before you wanted to send an email (no matter which method), then they would already have been moved out of the list's 'Active' tab and into the 'Unsubscribed' tab.
If someone resubscribes organically—through a subscribe form or through the one-at-a-time API request—then they will be back in the 'Active' tab for that list again, however their email address will still be present in the Suppression List.