I assume you mean teeth like people/dogs have, and not teeth in the way that many birds already possess, right? Having evolved from reptiles, many birds do already have teeth. Ultimately the lower beak doesn't tend to do a lot more than house the tongue and those teeth. Here's one example:
Assuming you mean a species with large beaks and jaws that could support human or dog-sized teeth...
Case 1 - No Teeth on Either Jaw
If there are no teeth on either jaw, this animal is going to need to eat things without mastication. That would probably restrict it to soft meals like VERY soft fruits and/or worms. A diet of that sort does not lend itself to needing or being benefitted by a curved beak, so this case seems unlikely.
Case 2 - Teeth only on the Lower Jaw
If there are teeth only on the lower jaw they are not going to have anything to match up with or go around on the upper jaw. Tearing would be a challenge since all of the mechanical force would be on only one set of teeth, so the animal probably wouldn't be tearing at much meat. Grinding actions definitely require something for the lower teeth to mash up against, which really just creates an upper set of teeth (or tooth-like flats in the beak), so being a herbivore is out.
That leaves a diet primarily consisting of a wider variety of fruits and bugs than Case 1. For the amount of stuff that gets stuck in teeth and their likelihood of breaking though, I think this animal would probably be out-competed in the wild.
Case 3 - Teeth on Both jaws
In a very real way, this starts to feel like the question "would a dog or person be benefitted by having a beak instead of a nose?". The short answer is that if we are it isn't apparently worth the cost of production. That is evidenced by the fact that it doesn't exist anywhere.
Curved beaks in particular are used for ripping, tearing and shredding... things that a good set of teeth can already do. It's a duplication of effort, and that is not usually rewarded in nature.