Well, yes, iodine is needed in quantity by the thyroid gland, so hypothyroidism can be caused by lack of iodine, and hypothyroid slows down ALL processes.
I was looking for something that links iodine and B12 specifically, and methylation generally.
I'm on T3 in vast quantity, so hypo-t shouldn't, in theory, be an issue for me, though I suspect it still is (temp still sub-normal amongst other things).