A plugin is really just a series of functions, possibly inside a class, so theoretically you should be able to execute it anywhere you want. But I’d guess that most, if not all WP plugins, depend upon too many WP functions to make it practical.
I have been able to extract the output of my plugin and shwit on my website.
the tip is to create a simple php file which could be called from outside of the wordpress loop. the thing that you need to remember is that this file should include (wp-load.php), and after that you don’t actually need to worry about any thing.