It's possible that some of the fugitives profiled on The Hunt can be caught. Given enough media attention, all it takes is someone noticing that a person they see looks like one of the wanted folks. Stranger things have happened. It's possible that through a series of coincidences, some of them can be apprehended.
On "America's Most Wanted" John Walsh has been credited with bringing to justice more than 1,200 fugitives, as well as with finding 61 children. This shows beyond a shadow of a doubt that broadcasting to Americans that a person is wanted by the police for heinous crimes increases the chances of that person being captured and brought to trial. John Walsh might not catch every fugitive, but there is no doubt that more criminals will be caught because of his efforts.
John Walsh actually had a lot of success when he hosted America's Most Wanted and I believe this show will be the same. If they have decent viewership I think they stand a great chance to have someone that knows something call in to give a tip. I know that after people watch those shows they are much more alert of the people around them.
Justice has to serve, in one way or another, and so the fugitives from the Hunt will get captured. The world tends to work in a certain way, towards good, even though bad things happen, and part of the world going towards a good direction is getting these missing people to justice.