You can definitely do that with a new template tag that fetches your random testimonials. Once your tag is added you can create a new temaplate to output the testimonials how you like.

Here’s an example of how to add the template tag: https://gist.github.com/TravisBallard/74377500c03cfd29d2cf

Heres an example of my output template that only outputs the author names in random order: https://gist.github.com/TravisBallard/23bf1c133b6b014d2dee