It is possible..
Our hormone levels fluctuate on a 24 hour cylce, the lowest ebb for hormone activity is on adverage at around 3am in the morning... Then they slowly increase before we get up in the morning, most people this rise doesn't really impact on their blood glucose leves, but others do find that they have impact on their levels.. The only why to find out is to test, at around 3am in the morning, then every hour to track the rise.
But what also could be happening is that the food that you eat the night before could be still be impacting on your blood glucose, this is more likely if you have a protien and high fat meal. quite an high percetage of protein breaks down into glucose adding fat to this can slow it a bit more, durning the day when you are moving around low level exercise general stables this all out, but over night it could rise the bg's...
If it's DP you would get the same effect/data will be the same every day, if it's food related then you would see days differing from others..