This is a rather strange question to ask somebody else to answer for you, because really it depends so much on what you think as you read the story. All I can do is provide you with my answer, but you will have to read the story yourself to come up with your own personal answer to this question.
When I first read the story, I wasn't too sure what was going on, especially towards the end. I did believe he had escaped, but then the descriptions we were provided with became increasingly bizarre and somewhat surreal. Consider this description in the last few paragraphs, once Peyton has supposedly "escaped":
At last he found a road which led him in what he knew to be the right direction. It was as wide and straight as a city street, yet it seemed untravelled. No fields bordered it, no dwelling anywhere. Not so much as the barking of a dog suggested human habitation. The black bodies of the trees formed a straight wall on both sides, termination on the horizon in a point, like a diagram in a lesson in perspective. Overhead, as he looked up through this rift in the wood, shone great golden stars looking unfamiliar and grouped in strange constellations.
Because we see what is happening through the eyes of Farquhar, we would expect the landscape to be familiar, especially because he is not far from home and he knows this road. Instead, note how words like "rift," "unfamiliar," "strange" and "black bodies" possess a nightmarish, surreal quality. These kind of details made me suspect that something was going on, though I hadn't actually guessed he was hallucinating until I reached the final paragraph.