No, it will not!
The small java script that enables UserReport to work will NOT slow down the load time of your website. The UserReport java script is what is called an asynchronous script – Just like the newest edition of the Google Analytics script, which you probably have installed on your website as well.
There are many advantages of using an asynchronous script, but most importantly this script type is not able to interfere with any of the content of your website or slow down your load times.
The asynchronous script from UserReport will always be the last thing to load on your website. This means, that it waits for other content like articles and pictures to fully load before it loads itself. The script should be placed in the HEAD or BODY section on the front page and all subpages of your website.