The primary purpose of the Teleport Platform is to redirect traffic. It is designed not to interfere with your site processes and not to change your users' experience.
In the event of platform disruptions, the script naturally turns off and does not interact with the site. All the content is broadcasted via CDN as usual (as you have not already turned off?).
You could test the Teleport solution on an insignificant amount of users, and we all will see how it works with your audience.