Last I checked the policy for uncaged falcons on QR is the following:
1. Falcon and handler must be in economy
2. Falcon and handler must purchase a block of seats usually along the window
3. Falcon must be hooded and leashed
Therefore on QR at least you wouldn't be sitting next to one. Being around falcons a lot I can say that the chances of you getting hurt are pretty much non-existent especially with the precautions taken above. The only disturbance you might experience is from the bird occasionally flapping it's wings and the handler will try his best to avoid that to protect the valuable birds.