I've never booked seats based on status, but have booked on United, AA, BA, and AF, and Delta. In all cases I've been able to either pick my seat online, or call FBC and have them do it.
But status usually involves and upgrade from whatever seat comes with the fare you purchased so it makes sense it needs to be fully ticketed.
And, I've only done business on BA and AF, so unsure how economy would work with them.