Well, this probably works. 
But if you have SSMS 2016 (16.3+) installed you can just use the Get-SqlLogin cmdlet.
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foreach ($RegisteredSQLs IN dir -recurse 'SQLSERVER:\SQLRegistration\Database Engine Server Group\' |
WHERE {$_.Mode -ne 'd'} )
{
Get-SqlLogin -ServerInstance $RegisteredSQLs.Name -LoginName BobbyTables
}

Granted, if the login doesn't exist you'll need to wrap a Try/Catch around it to get nice, pretty output, but it works.