If I'm going to use a play off "Let's Get Dangerous!", this really ought to be a Darkwing Duck post, it's not. The first thing I thought of when Ragdoll said he had no soul was Kevin Smith's revival of Green Arrow.
If you haven't read it, we learn that just before Parallax Hal "died" reigniting the Sun, he brought Oliver Queen back to life. Except Ollie's soul didn't want to leave Heaven, a surprisingly intelligent thought for Green Arrow. So Hal did some handwave stuff about building a new body out of whatever was left after Ollie was blown up, but cut its memory at the "Hard-Travelin' Heroes", and then left it to figure things out. Since Soul Ollie stayed in the afterlife, it was a body without a soul, which lead to fighting with Jason Blood and Etrigan, and demons attempting to take over the body, and so on.
So I'm a little curious why demons don't seem to have any interest in trying that with Ragdoll. I'm not sure how long passed between Final Night and when resurrected Ollie learned the truth about himself, but I have to imagine Ragdoll's been alive a bit longer. Surely he would have been a viable target also.
I get that he's a potential savior (or has been told he is, this is Hell we're talking about). Even if that's so, I imagine there are denizens of Hell who don't want a savior. Why wouldn't they either possess him, or trick another demon into doing so, hoping to put the kibosh on the whole thing?
Another thing occurred to me as I was typing this. Why didn't Resurrected Ollie start to develop a soul? What I mean is, there was an issue of Teen Titans where Raven showed Superboy (Conner) his recently emergent soul. I guess being a clone he hadn't had one until he overrode Luthor's control of him in the previous story. Again, I'm not clear on how long Conner had been alive/active? by that point (it was around the time of Infinite Crisis lead-up), so maybe Ollie needed more time. It didn't wind up mattering since Soul Ollie eventually left Heaven to save his son, though that could have been strange, the body having two souls, both Oliver Queen, but not the same.
That makes me wonder if perhaps Ragdoll had been possessed, by demons either guiding him towards being a savior, or away from it. Then he saw how much Alice cared for and relied on him, and that prompted a change in him, a soul coming into being. It drove the demons out - which might explain his not hearing voices anymore - and this new soul sat there and saw what the person it inhabited had been up to this point and didn't particularly like it. Rather than follow his new Jiminy Cricket's advice, he opted to flee to Hell, perhaps get back in touch with what he feels are his proper roots.
I'm trying to pull together a theory from three separate stories, by three different authors, spread out over a decade. I ought to leave that stuff to Roy Thomas.