We are adding the Pardot tracking script to some of our pages. Looking at the JS, all it does is set a couple of variables and load a further JS file (https://pi.pardot.com/pd.js). Is there any reason why we couldn't host the pd.js file ourselves?
There is no reason why you couldn't include the script in your VF Page, it may not work as well with Lightning components so I would check for conflicts. Also various security protocols may cause issues including remote scripts in Lightning components.
You could include the JS file as a static resource which would make it static to your resource file, but you would have to make sure to update it with Pardot's API