Seaweed has selenium as part of it. It also is a great source of bromine. My feeling is that seaweed is a good supplement; but not for Iodine therapy as tought by the "iodine expert doctors". That therapy requires that Iodine is not interfered with; until it has done its job.

Saying that, means that you should not take any anti-oxidant close to the time when you take an oxidant, like Iodine or even oxidated water therapy.

looking at it in this way...
During digestion everything is brought into solution in the stomach consisting of HCl.

The element Iodine normally exists as Iodide in nature, however other common forms include potassium iodate (KIO3) and molecular Iodine [I2]. Iodine is relatively insoluble, but this can be improved by complexing the iodine with Iodide to form triiodide [I3].

Iodide/tri-iodide in the presence of acid [HCl], will form molecular iodine [I2].

This iodine reacts rapidly with vitamin C in solution. Iodine is reduced while vitamin C is oxidized.

So, I personally would avoid washing down my sushi wrapped in seaweed with ascorbic acid + water. Just would take it at separate times.[im0]
http://www.chem.ubc.ca/courseware/123/tutorials/exp14A/
http://www.wcaslab.com/tech/iodine.htm