Ezoic in no way interferes with how Google indexes your content. The content doesn't move location - all the content on your pages remain in exactly the same place, none of the content changes and none of the backlinks change. Everything stays exactly the same, it's only that the layout has changed on the page.
For all the sites in our platform (with over 18m users accessing content per month), we have a 99.97% score from Pingdom for 'up' time (which is very good). This is because we use AWS (Amazon Web Services) to serve your content for you - with 4 data centres around the world, so your site is almost always going to be 'up', no matter how many users you have on the site.