I am going to speak indirectly to this, kind of...
I don't know the physiology of nocturnal erections but mine have increased. I used to think they were caused by the body stopping urination while sleeping. But I stopped having them for years and I didn't wet myself in bed so that idea doesn't hold up.
I don't think I was having trouble getting an erection before in regards to intimacy and sexuality. But the fact that I am getting way more erections when I wake up at night SINCE i have been on iodine, tells me the hormonal nature of these night time erections, because Iodine makes all the hormones work better.
So, I can't say for sure this will work for you, but I would guess it is certainly worth a try.