Yes it will. Topically apply iodine, either drops of Lugol's or the drug store variety that contains alcohol. Some people "paint" them with Lugol's and a q-tip type thing. Iodine is an anti-fungal, antiviral, and antibacterial. Considering that a wart is viral, this will work nicely. You could probably get away with using and organic iodine; especially if you have allergic reactions to Iodine on your skin.
It may take a about 2 weeks. You will want to continue painting the spot after the wart is gone. At least for a few days. You may want to cover it too. I have not. I would not mess with genital warts though. I've heard that it is not the same thing.
The problem with warts is that the virus can remain in the body and cause the warts again. Internal use of iodine can help; just don't use the alcohol based iodine.
I don't know about killing the external warts by internal use of iodine. It may help you to know that the skin is one of the organs that stores iodine. The virus that causes the warts will be killed by Iodine within the body; so, that will help too. I just don't know the amount of Iodine you would need for this. I suppose it can have some effect on the external warts; but I'll bet that it will be slow. Please be aware that the alcohol based iodine (drug store variety) is too dangerous to take internally. It is the alcohol; not the iodine.
I think you may find a cream that could help the process along. I understand that you would not want to have the iodine stain on exposed body parts.
Check with wombat on the iodine supplementation forum. She has made a salve with iodine as the main component. Some have reported success with other skin problems with this salve. She could give you the recipe.