Solution:
Creating a custom php page that will be able to be viewed in any theme (and have the theme applied) would be considerably difficult.
Each wordpress page calls specific theme functions of that particular theme, as well as referencing files of that theme to generate header, footer, css files, javascript files, etc.. Your custom page would need to plan for all of these contingencies, for each possible theme used.
Here’s a alternative solution: inject PHP code directly into a standard wordpress page via this plugin http://wordpress.org/extend/plugins/allow-php-in-posts-and-pages/
Meaning: you make a normal wordpress page, but are able to add php to it. When this page is rendered, the proper page template is used, and all the theme references are taken care of for you.