Basically I’m with Wolverine.
Releasing when the animal is dead could be an option and even an advantage, but what if it is just wounded?
That is where the breeding comes in. Dogs should be so selected that they are not too shy nor too agressive. That is why pedigrees are so important, an expert, certainly not me, can see at a glance what he is looking for.
Would the dog alone stop the deer?
Yes, when it is properly bred and trained.
But what if even with a dead deer, the dog finds it and comes back without willing to get to the deer again.
Training, Training and training.
I have a friend who almost always lets his BMH track free, 90% of their tracking is Ibex, and his dog carries a GPS collar. Ibex is kind of different as will climb onto inaccessible places while wounded, letting the tracker arrive and shoot. I’d consider using a GPS collar if unleading is usual.
BMH were specifically bred to work off the lead in the Alps where the work was regarded as too dangerous for the heavier HS. Delighted to see your friend picking up that tradition again.
I’d never release while tracking boar, female or male, with a courageous dog. Some less courageous ones could be released if you know that your dog will stay a few meters away of the boar. But you have to know very well your dog’s reaction in such circumstances, so again I rather track on a leash first.
As above, training will show you. A few people in Germany and the Flemish Tracking Society have a tame boar to teach their hounds. Wonder if a Jamon Iberico pig would be more attractive for a dog? I certainly like the smell.