Edit: It turns out you can catch your own removing event through a LocalScript and listen for chat commands, even after the script is destroyed. +1 to HexC3D for the effort.
This is more of a hypothetical question, but is it possible for the server to receive input from a user whose player object has been removed, but still exists as a NetworkReplicator connected to the NetworkServer? My intention is to create a way for my moderators to join a server and monitor chat without anybody knowing they exist. Can this be done?

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From what I've tested, a player can still exist as a floating camera when their player is removed, as long as there are other players in the game. If there are no players on the leaderboard, the server instance shuts down.
Hmmm, let's test that out.