Regarding breaking your site; there's nothing that can't be solved with some configuration, have a look at the troubleshooting-section in the FAQ.
Regarding AO making your site slower; initial page load can indeed be slower (depending on how much JS/CSS you have and on cacheability of the optimized CSS/JS, cfr. FAQ for that as well, it can be between 1/10th of a second and a couple of seconds), but as soon as the page is cached in cachify, you should see the page being faster actually.
frank