If someone owned several acres of woodland area that was fenced off from the public, could a dog go for a walk without the owner?
No, dogs don't walk themselves.
As lila already explained in their answer, dogs are social animals. If they grow up feral, they live in packs with several animals. If they grow up with humans, they live together with at least one, often several humans. They need this company to be mentally healthy and stable.
Let's imagine: You live with a dog in a nice house in a rural area. When the mood strikes, you open the door and let your dog walk into the fenced area. What would your dog do?
While it's in the house with you, it constantly interacts with you (even if this interaction is no more than a sideway glance) and is always aware that you, the pack, are nearby.
Outside, it would probably poop and pee, maybe even sniff around the perimeter and mark its territory. But since no foreign dogs can enter the fence, marking isn't as important as in the wild. Since you aren't around, there's no-one to interact with and nothing meaningful to do. Even if there were toys lying around, there's no-one to play with. It's booooring.
What incentive does a dog have to take a walk?
- Social interaction with the owner (who doesn't want to be with the dog in this scenario)
- Social interaction with other dogs and/or people (who cannot enter the fenced-off area)
- Mark the own territory (seldom necessary, since no foreign dog can challenge / overwrite the mark)
- Sniffing where other dogs peed, which is an indirect social interaction (again, impossible in this area)
- Hunting for food (unecessary since a full food bowl waits in the house)
The pack mentality is so ingrained in dogs that they won't be happy without social contact. If you fail to offer this social contact, the dog will not accept you as the pack leader (you'd be barely accepted as pack member), it won't follow your commands and will try to find another pack.
If you only offer social contact in the house, the dog will want to return inside as soon as possible. It won't burn off surplus energy by going on a walk on it's own but rather by eratic behavior and/or destroying things in the house.
If you're not ready to dedicate quite a lot of time and effort to your dog, please refrain from getting one. In reality you need to invest even more time than you initially thought or your dog will develop problematic behavior and make your live much less comfortable than it was before you had it.
I would say it's an interesting question with a bit complicated potential answer.
Allowing your dog to roam free on its own in some enclosed private area, considering there are no hazards like deep pits your dog could fall into, etc. would of course be better than keeping it indoors all the time. Dog for example wouldn't rely on your presence to be able to take care of it's physiological needs.
On the other hand, walking a dog is not just about its physiological drives: mainly it's about exploring, interacting with novelty and fulfilling cognitive needs. Dogs are intelligent and their minds are complex enough that, sooner or later, any enclosed area would ultimately prove to be relatively dull and uninteresting compared to all these unfamilar and exciting temptations existing on the other side of the fence. It could lead to development of anxiety and wide range of mental issues.
Also, please consider that dogs are social animals. Letting them loose in an isolated woodland would provide them space and fresh air, but probably close to no interaction with other dogs and people - generally almost no social stimuli compared to "manually" walking it in public, outside of your belongings. What is more, if you have a healthy relationship with your dog, it sees you as the leader of the pack - and for this reason feels safer, more secure, and I guess just more cheerful while walking around with your companion because it feels like it is sharing its cognitive experience with you which is a powerful and positive social stimulus.
In essence I would say that it's really convenient and also beneficial if you owned some land or otherwise had some safely enclosed outdoor backyard that your dog could use - and (excluding any potential legal concerns I could have missed) in that sense I'd say yes, a dog could somewhat walk itself but only if we consider walking a dog as an euphenism for letting it go to the toilet. But that would never be the true substitute of "manually" walking your dog.