They will die. All of my hinge cuts eventually die. The question seems to be when. Sure there are a few that live for quite a while and younger trees seem to live longer. Nutrients need to travel through a fraction of the cambium they had before the hinge. Often the connecting bark strip is supporting some of the weight as well. Often in time it breaks further. There is now a lot more exposed surface area to dry out and die.
Hinge cutting, in my opinion is a short term solution. It can provide instant cover and in areas with little food within reach of deer it can instantly add quite a bit of food. It opens the canopy which further increase deer food a bit more over time.
If you don't need the instant food and cover, I like the idea of logging better. You can do either select cuts or clear cuts and, depending on how much you have, make it a positive cash flow operation. Logging hardwoods will create what MSU Deer lab calls "Mineral Stumps". This is simply the stump suckers that are produced. Because the large root system is feeding a much smaller amount of top growth, minerals and nutrients are much more concentrated in those suckers and deer seek them out. In select cuts, you can eventually use herbicides to kill the stump suckers before the form multi-trunk low value trees. Controlled burns, especially in clear cut areas are anther tool that produces good deer habitat.
There are situations where hinge cutting works well, but in most cases, I prefer other management techniques.
Thanks,
Jack