I don't think there's any way to extend SQLPS and/or SMO to include LocalDB instances on the list of SQL Server instances. Currently SQLPS and SMO don't understand LocalDB instance model, just like (I think) it didn't understand User Instances of SQL Server Express before. Also mixing regular and LocalDB instances could be confusing to end users. LocalDB instances are per-user and only visible by the user who owns them, so different users would get a different list on the same machine. Regular SQL Server instances are installed per-machine, and all users see the same list.
I bet you could write your own PowerShell plugin or module. All you need to do is to call LocalDBGetInstances and LocalDBGetInstanceInfo functions from LocaLDB API (available through C/C++) plus the existing SQLPS or SMO for the regular SQL Server instances. I'm not sure how you distribute such plugin though.