Not really. This index.php is just a wrapper as it will refer their .js/.php which you have no control of. To use it fully you'll have to write those as well, at which point you can just start from scratch on your own terms.

So is it running arbitrary PHP on my server if I run this?

Of course not. Index PHP contains ALL the PHP, while CSS and Javascript are loaded into the browser for the interface.

Something like that.