You're basically talking about Cryogenics, its an actively researched field at the moment. maybe your wanting it without the freezing part, but there are several other questions about cryogenics around that i would just be copying so i'll just answer your questions instead
Will it help reduce resource usuage... No, not only would it take some of those depleting resources to build the machines, but would likely take a lot of power and possibly other things to run them, using up yet more resources. then you'd have all the people that need to run the facility where it takes place, taking up more, and then the facility buildings themselves all around the world, each requiring resources to maintain let alone the infrastructure beyond these points
Will it be possible in the future... possibly, its being researched for making extra planetary trips more realistic, why support a generational spaceship for a few hundred years to reach another planet when you could have them sleep for that time instead.
Could this allow Equality
Most definitely not, this sort of thing wold be heavily abused for profiteering, who makes them and maintains them? someone has to pay for it, the machines would probably be expensive to build and run so it would be an expensive treatment therefore only the wealthy would be able to afford it, remember if you're asleep for even 10 years, thats 10 years where you are not working and therefore not earning money, so unless you you own a business that can be run by other parties while you sleep, then you won't be able to afford to do this