By what you are saying, it sounds an high probability indeed..
Other signs that you might get which suggest night-time hypo sleep through can be
Feeling lethargic, headache,visual disruption the feeling you've been drinking when you haven't touched a drop..
I would do some night time testing, to see how your basal line is reacting overnight..
You can either go the whole hog and test on one night, or split it over several nights with caps in between...
One of the result to look at is the one's around 2am-3am as this is likely to be the point your body hormone production is at it's lowest ebb so will you blood glucose..
Also by doing this, you can then take a look at whether Dawn P is playing any part, this is where your bg start to climb early morning, but it will be a consitant rise every morning rahter than only every so often..
Another thing to consider, is what happen in the day before you had the night time hypo, as it could be caused by delay reaction to exercise or change in routine, even foods that you have eaten could be still effecting your blood glucose in the morning rather than you having been hypo... Pasta, pastry high fat foods all can have this effect