More to the point, would Uriel be allowed to cure Thomas?
Exactly, that is the question for all eternity for archangels.
Also, I'm not sure if Uriel could separate the parasite and Thomas without turning Thomas into someone else. It comes back to the question of how much of Thomas comes from the human and how much from the presence of the parasite.
I think the answer is both simple and complicated at the same time. Uriel is all about free will, he might be able to blow away an entire galaxy if he wanted to.. However he cannot because he is under orders not to unless ordered to by his Boss. Archangels don't have free will to act, that's why one of his fellows by the name of Lucifer now resides in Hell, he thought he had free will and fought for it. So yes, I think if he wanted to, Uriel could get rid of the Hunger Demon, but he isn't free to act on his own. It's like in Changes when he agreed with Harry that he could fix his broken back, but there are rules for doing that, and Harry didn't qualify under the set of rules. However since a fallen angel influenced Harry's free will, Uriel was able to step in. Back to free will, as we know the Hunger Demon cannot take root until the young would be vampire chooses to have sex, feeds during that sex until death of the victim.. Lots of compulsions there and teenage hormones, but it still comes down to choices. We know that true love will burn out the Hunger Demon, which was the hope Thomas and Lara had for their little sister Inara. However I don't think there is any information on whether celibacy past a certain age eventually kills the demon/parasite. Celibacy is a life choice that Thomas didn't make, however in his case there might be some loop holes as far as free will goes. Lord Raith did set his son up like he did all his children to end up having sex once puberty sets in knowing that in most cases it will be until death, from then on the Hunger Demon/parasite takes over. We know that Lara has said that she is happy being what she is, she wouldn't chose anything else, she accepts it. However while he did go through a time when Thomas almost starved himself when he was living with Harry, and Harry saw that struggle in the soul gaze, have we ever heard Thomas say if he had it to do over he'd choose to be a vanilla human? Interesting that both he and Lara wanted their little sister, Inara to understand and have that choice. Lara says she wouldn't change a thing, Thomas isn't quite so clear..
So could Uriel do away with the Hunger Demon/parasite? Absolutely.. Can Uriel do away with the Hunger Demon/parasite under the rules governing archangels? Probably not.. Is there a possible loop hole here? I think so, but it is complicated..