I've just tried this setup on my dev machine with the code from SimplePie's documentation (http://simplepie.org/wiki/setup/sample_page
): it works like a charm, I confirm.
No need to modify index.php, the include statement can be in your custom PHP script (the one you call from your actual snews page). You just have to take care of the actual path of simplepie.inc. By the way, you don't have to put it in specific dir (like "php" in the documentation), it can live in the same dir (root) as index.php and snews.php, no worries.
For example I've put it in a "simplepie" dir and I've renamed it to simplepie.inc.php: it still works as expected.
Same thing for the 'cache' dir: by default it has to be in the same dir as your custom script, but this can be changed by editing simplepie.inc, line 490 (the path is relative to your custom script, not simplepie.inc itself because of the include statement).
The ball's in your court! :-)