Yes, SQL Buddy supports Nginx. If you would like to test SQL Buddy on Nginx, try FusionLeaf Stack. The instructions are here:
http://code.google.com/p/fusionleaf/wiki/stack_instructions
Emmanuel also makes a good point. Try creating a simple test page to see if PHP is configured correctly with Nginx:
<?php
echo 'Hello Word';
?>
All you should see if Hello World if you try to visit the page in your web browser. If you see all of the code on the webpage, it means either the last block (location ~ \.php$) in your nginx .conf is not configured correctly or PHP is not working properly.