If I load a PHP page with Jquery .load(file.php), can the included file use the php variables that were defined on the page that called the load()?
You would have to pass those variables to the loaded PHP file through the .load function.
Example:
$("#objectID").load("test.php", { 'choices[]': ["{$choice1}", "{$choice2}"] } );
The variables defined in the current PHP file would become part of the Javascript that loads the new PHP file.