Some people may drop low and then rise but it seems as if it may be rarer than people think.(and talk about) In the last few years they've researched it using continuous monitors and haven't actually been able to find it happening. They've found that undetected lows overnight normally result in low not high morning glucose levels.
Here's the abstract of one of the most recent studies.
Do high fasting glucose levels suggest nocturnal hypoglycaemia? The Somogyi effect—more fiction than fact
http://onlinelibrary.wiley.com/doi/10.1 ... ated=false
The only way to really find out what's happening overnight is to test but personally I didn't really find out what was happening overnight was until I borrowed a continuous monitor. I've now done that three times .
Personally, I think that what I did/ate the day before has a big influence on results next day. (less exercise, higher glycemic carbs, higher fat will for me result in 'dawn phenomenon, more exercise, less carbs/food may result in overnight lows so I need to adjust for those; I use a pump) I've also found that when I go low I rise a couple of mmol/l and then can even fall low a second time; morning levels end up low).