This article reviews many of the aspects of seaweed consumption in the Japanese population. It also discusses the effect of combining seaweed with cruciferous vegetables and soy (which can counter-balance iodine), as well as certain seaweeds that concentrate bromine instead of iodine.  There is no discussion of relative forms of iodine, such as molecular iodine I2 vs iodide anion I-. Seaweed probably contains both forms, which would be similar to Lugols.  (click here for more on the forms of iodine).

Assessment of Japanese iodine intake based on seaweed consumption in Japan_