No, you can't use Google Play Services on the Unity Java Plugin. The Google Play Services API is designed to be used in native Android apps, not in games created with Unity, so it's not available for use in Unity.
However, you can use third-party plugins which can provide basic features like leaderboards and achievements for Unity game developers. For example, the Everyplay Aura plugin for Unity is a good option for integrating leaderboards and achievements with Unity games.
If you are looking for Google Play Services specific features like in-app-purchases, push notifications, etc., then you can look for third-party plugins that integrate with Google Play Services for easy integration with Unity. One such option is the Google Play Games Plugin for Unity, which provides easy integration with Google Play Services for in-apps-purchases, leaderboards and achievements, cloud storage and more.
I hope this helps!