Is it possible to enter PHP code on pages in SCCP? For example, I could do an include of a file containing the code generated by menu builder:

include('includes/inc_nav_upper.php');

In the shop settings, I can include links to the css and js files for the menu. If there is a way to enter the php, that would make it very simple to add a menu builder navigation menu.

Not if your shop is hosted on S-Drive. Otherwise You could place the code on your page and use a little css or jquery to render it correctly. You may have to alter you .htaccess to parse php inside html.

Does S-Drive support PHP and MySQL?

Only for internal systems Brian, it doesn't support user uploads of any. You can use CC software such as Form Builder and Shopping Cart, but the PHP that is utilized is internally written by CC itself, you cannot upload, embellish etc. any of that code at this time. Not sure if they plan to free that up later or not, rumors have it that it will be, but not sure if that's true or when it would happen if it is true.