How does running a remote MySQL host impact MySQL services ?

Using a remote MySQL setup, will be functionally the same a using a local setup. Since you are configuring all your customer connections to occur over tcp, the only difference will be their connection string. On the backend, the only applications that are connecting with domain sockets are horde, squirrel mail, and phpMyAdmin. All these connections are built dynamically from system variables determined by your configuration. All service status information should be displayed normally. In short, running a remote MySQL host will have little to no impact.