I'm not sure if this should be posted as a bug or requested as
a feature, but I think bug as maybe it was just an oversight
after multi-server was added.

In the options dialog, when you select/deselect Invisible mode,
it sets/unsets invisible mode only on the active connection, but
it selects/deselects Invisible mode on all connections. I would
think it should effect all connections and not just the active.