Does the functions.php file ever get called during an AJAX call? Debug AJAX

Trying to figure out an issue a fellow programmer is having. I was wondering if the functions.php file get called at all when you do admin side AJAX? I know that when you do an AJAX call a part of WP gets loaded up to process the call and send back a response. Is the functions.php file included in that?

How can you check if you are in a particular page in the WP Admin section? For example how can I check if I am in the Users > Your Profile page?

I’m building a plugin and I want to add bits of javascript in the admin head but only for certain admin pages. I don’t mean pages as in a WordPress page that you create yourself but rather existing admin section pages like ‘Your Profile’, ‘Users’, etc. Is there a wp function specifically for this task? I’ve been looking and I can only find the boolean function is_admin and action hooks but not a boolean function that just checks.