It's an interesting question, Nancy.
Depending upon the person and the situation, evil spirits can be behind the clutter and disrepair because they are the ones who brought the victim into a state of depression to begin with, and taking care of daily chores becomes increasingly difficult for them because there's no desire for living. This is the case with the old woman, for "although she did her best, she could not keep up with the day to day maintenance that a house that size required." I've gone through periods of depression, and it's always this way. You don't have any energy for doing anything, and yet the housework keeps piling up and you keep getting farther and farther behind, and the enemy uses this to make you even more depressed because of your surroundings. But when we are restored to joy and closeness with God, suddenly our energy returns, and the house starts getting clean and you start putting your affairs in order again. This also happens to the woman in the dream. The presence of God empowers her inwardly and then manifests outwardly, and the house gets cleaned up. It's yet another confirmation to me personally that the dream is from God.
Now I will say this, however. The old saying "cleanliness is next to godliness" is true in many ways, in how "the atmosphere changed and the house turned from an old, dark and dingy, neglected, demon infested hovel, to a beautiful, spiritually clean, peaceful, light, bright, shiny new home... The old woman had also changed into a kind, joyful, caring, loving, woman of God." But the thing that we have to watch is presuming that our joy comes from without, i.e. from keeping the house clean and our life in order. Certainly it's better for one's moods to have things beautiful and orderly rather than messy and in disrepair, but our healing as believers comes from the Lord Himself, i.e. from the power of God within, and not from anything without. If we lean on the wrong source for joy and strength, it's only a matter of time before it will fail. Many rich people are miserable even though they have a small army of servants to keep everything spotless.
Sort of reminds me of Jesus' teaching to Mary and Martha, and how Martha was busy doing all the cooking and cleaning, but Mary was doing the one thing absolutely necessary (Luke 10:38-42).
So it becomes a matter of making sure our priorities are straight, and we put first things first. So long as we do that, I think the saying has merit to it.