This is technically possible, but not very straight forward. You need to develop a proxy to convert the XML http request (from phone) to a SQL query to your database, and viceversa for the response.
Instead, I would recommend you to use the LDAP corporate directory feature on the phone, which initiates LDAP request to directory databases. It will be easier to integrate with your database, provided you have the right connectors.
It is 100% possible. You will need a web server with php in order for this to work. once you have that up and running you can set up a php to serve the database as an xml directory. Here is an example I did for asterisk that you can modify.
$mysql_conn = mysql_connect("localhost", "USER", "PASSWORD"); // change local host to the database you want to use, and change username and password
mysql_select_db("asterisk", $mysql_conn);// change asterisk to the database name
$result = mysql_query("SELECT name,extension FROM users", $mysql_conn);
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