I know that I can see who clicked through on the "donate" link on an email - but I don't see a way to check if the donation was made as part of that interaction.
Is there a way to determine this?
The easiest way to do this (whilst not 100% foolproof) would be to create a special donation page for the link in the email (i.e. separate from the donation page that presumably appears as link and 'proper' page on your website).
Go to Contributions >> New Contribution Page or Administer >> CiviContribute >> Manage Contribution Pages.
Then once your new contribution page is complete, simply copy the URL you get from Links >> Live Page into where you have the donate link in your emails. It will look something like https://your-site.com/civicrm/?page=CiviCRM&q=civicrm/contribute/transact&reset=1&id=2
As long as you don't link to that URL from anywhere else (like a button on your website), it should only ever be used by someone clicking on an email. You can then use a Contribution Report for that particular donation page.
It looks like you may also be able to do it with custom fields and passing URL parameters, but that's more complicated. See this entry in the wiki, from 2014: https://wiki.civicrm.org/confluence/display/CRMDOC/Update+custom+fields+in+contributions+and+events+by+passing+variables+in+a+URL