PHP is just a server-side programming language. You can use any language and any server. The main issue is
Can I Query MySQL Database Directly from Android without a Web Service?
Yes you can. Just open the port where your MySql database is set usually at 3306. You also need JDBC Driver to set up connection to it.
Should I Query MySQL Database Directly from Android without a Web Service?
Unless you want to make a Database Client app (like phpMyAdmin) where each user holds his own credentials then you should not. In such case everyone will be using their own credentials to access their own db. In your case, you'd be hardcoding your database credentials in the app for everyone to access.