The language of the Spell can be found
here. Most of its just mystical sounding words. The key parts I see are "Spirits of the
interregnum (a purgatory)," "Gods, bind him, cast his heart from the
evil realm (Hell/Tartarus)." "Let him know the
pain of humanity, gods." I point to these parts, they show who the Invocation is intended for, that is, the Powers of the Abode of the Dead, it describes what she is ask for, which is for his soul to be released from the Abode of the Dead and returned to his body, and for the intended effect, returning the soul will cause great pain. So, it's invoking the Gods of the Underworld, to curse a vampire by summoning a shade of the dead, then grafting it to the vampire, with the intended effect of torturing the vampire. I say that's dark magic, but I am by no means an authority on either magic or gypsy religion. If it was white magic, I assume the purification/destruction of the undead would be the goal.
As for the intent. I think the ensoulment was intended to drive the demon mad with guilt, that what was once a Prince of the Underworld is reduced to a pathetic rat eater. Maybe he would kill himself, maybe other vampires would kill him as he begged for death, maybe the humans would get him. As long as he suffered. I don't think the happiness clause was of any weight to either party. I mean, I assume for a spell like this, the Witch had to act as shaman, had to negotiate the terms with the Gypsy ancestral spirits, and this was seen, if he did achieve happiness, if his pain was lost, more pain, he had to watch those he loved, die at his own hand. Remember, some part of Angel is always with Angelus per "Orpheus." Granted, I hate that scene, it destroys the rest of soul canon, but I suppose it is in alignment with this idea. But I think the idea, it's not going to happen, he's going to be eating rats.
As for Willow's use. Angelus, when he returned, killed both Enos and Jenny. The Gods in question should have been happy to avenge them. In season 4, if D'Hoffryn was any indication, all the Dark Forces of the Night were in awe of Willow Rosenberg, she had their respect. And again, my understanding is limited, but in Magic, power is power. The ability to talk to the spirits is what matters, not which spirits you talk to. However, I do think if she started using the spell every time Buffy and Angel hooked up, the Spirits would just Zap her.
Finally, it's worth considering that Angel has a destiny. A vampire with a soul is rare thing, and both sides have evidently been cultivating him for his role in the Tro-Clon. Given what we learn about Jasmine, these guys work on a very long time scale.