OK, my curiosity was sufficiently piqued.
For a Duemilanove (just one...mine...there might be unit-to-unit variations):
With a 9V power supply only (no USB), current consumption is 26mA.
With USB only (no power supply), current consumption is 35 mA. This was measured with a DMM after fuse F1 was removed (the DMM measures in series with the fuse).
With both the 9V power supply and USB plugged in the current consumption is 35mA from the power supply only.
So it looks like the FT232 does enter into a partial shutdown mode when there is no USB data, but still consumes current.
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