Thanks for your question. The Covenant Eyes app only functions as a browser on the iOS platform. For all other devices - including the Mac - Covenant Eyes is simply a program that runs in the background. There is nothing to open. And yes, it will still capture screenshots inside the Safari browser on a Mac. On Mac you are free to use common or standard browser apps like Safari, Chrome, and Firefox without issue.
In case it would be helpful I am including a link to an article that shows you how to make sure Covenant Eyes is working properly on each device. You can find that article here71.
If you have any further questions or concerns please let us know. Thank you and have a great rest of your day.