It shouldn't have a noticeable impact on the site, since it just mimics what the plugin does while building the list on the back-end. Also, WPP has been using AJAX all along - the whole views count updating part was done with AJAX.
From v2.3.3 and on, AJAX is now also used on the list itself - the script requests WPP to build the popular list, WPP then returns the HTML markup and the script injects it on the site. This is to prevent plugins such as WP Super Cache from caching the entire list because it would never be updated again. Fortunately, this feature can be deactivated at any time so I'd say it's worth a shot - so if it does slow down the site, just disable it.
Anyways, since you asked about performance: I'm also planning to add some sort of caching feature to the plugin itself. I'm studying a couple of possible solutions that should really speed up the plugin and lower the impact on the DB.
Edit: ah, thank you Sam! I see, in that case I'll be needing your help in the upcoming days. WPP 2.3.6 is already in the works, I'll make sure to add WTC 3 to the TODO list and post here one or two test versions of the WPP plugin so you can help me out with this, alright?