The human body can survive for a pretty long time without food or water. A famous example, Mahatma Gandhi, survived 21 days with only small sips of water.
However, that's with a bit of water. According to Scientific American, the human body can last (on average) around a hundred hours without water, at the far end.
However, this depends on the temperature, humidity, and other environmental factors. Madeline was put into a tomb underground, where I assume it was cold and damp. There was a storm outside, so that wouldn't help. Maybe she was in a tomb instead of an actual coffin?
When Madeline's body had been placed in a coffin, Usher and I alone carried it to it's temporary tomb. This was a vault, or compartment, in the foundation walls of the mansion. It was small, damp, and without any light. It was directly under the room in which I was staying.
It's highly unlikely she'd be able to survive without any water for 7 days, even in those conditions however. It's more likely that there was a small trickle or pool of water in the tomb and that she wasn't confined to a coffin.
TL;DR: Not really feasible, she had to have some water. Either Poe made a mistake, this is a different universe, or Madeline became some sort of zombie who didn't need water.