Touching one's own dæmon would not be effective, as it is (like you said) a physical manifestation of their very soul.

However, should someone come into contact with another person's dæmon, it will have the same effect as touching the person that the dæmon belongs to on what feels like a magnified level to the owner of the dæmon being touched. It will feel like energy is literally being transferred into them, as opposed to simply getting it and barely noticing it with normal contact.