In general, no.
Inheritance is for IS-A relationships. You should inherit when you want all the methods of a class to be usable by its extended class.
Do you want calling code to be able to do this:
$user = new User('mysql:host=localhost;dbname=test', $user, $password);
$stmt = $user->query("SELECT * FROM Comments");
In other words, by giving access to general-purpose methods like query(), you allow someone to use the User object to query any unrelated data. That would be very confusing!
As @zerkms says in a comment, "User is not a database [connection]". That is what would be implied by User IS-A PDO.
This is a case where you should favor composition over inheritance. Each of your domain model classes, should HAS-A PDO object, which would give you an opportunity to avoid repeating code in every class.
Your usage would therefore be:
$pdo = new PDO(...);
$user = new User($pdo);