Stop! There's 131, 132 and continuing degradation of 132Te.
The iodine content of the thyroid is not due to a dynamic equilibrium from being in solution. It is actively transported into the thyroid. That depends on the need for iodine.
The iodine content of the thyroid (of an adult rather than working with the variation by age of children) is around 20 milligrams. And the typical daily iodine uptake is around 120 micrograms.
If the thyroid has taken in one day's worth of iodine that happens to be radioactive, then the effective washing out of that could even be slowed down by further iodine uptake! You really need to see detailed, atomic level iodine movements within the thyroid lumen to know.
You could imagine a thyroid that is, at the start, slightly low in iodine. Along comes some radioactive iodine, possibly more than is usually available, and it is avidly transported. But by the time the prophylactic iodine arrives the thyroid could be replete and uptake at a very low level.
As I said, I'd want to check detailed research before accepting either story of what happens.