I would be looking at specifically how your horse is pulling. The aussie noseband will help stop him getting his tongue above the bit but it wont stop him crossing his jaws, opening his mouth etc, so you need to look at what he is doing when he pulls. But yeah the aussie noseband will not specifically stop him pulling, just lift the bit and stop him getting his tongue over it.
My mare tends to cross her jaws and pull when she gets hot and I find what works for her is a high ring grackle - which are comfortable and excellent for eventing because they don't restrict the horses breathing. BUT it wont work for every horse. She doesn't pull with it on, and it works for her.
Is your horse opening their mouth when they pull? Tongue over bit? Crossing jaws? It's pretty rare for them to just straight out pull, mouth closed etc.