If he's drinking a large amount of water he's most likely hyperglycemic and when he's shaky he's most likely hypoglycemic. So yes, it sounds like his blood sugars are quite unstable.
Does he go "hypoglycemic" when he hasn't eaten anything? Typically when diabetics are untreated the tendency is to go high rather than low, so you could be looking at something other than diabetes, possibly. The best thing to do is get an A1c test done and get his fasting blood sugars tested. You might also want to look into a glucose tolerance test as well.
Has he gained or lost any amount of weight lately? When I was diagnosed I had lost a lot of weight out of nowhere because my body wasn't getting nourishment from the food I was eating because I had no insulin in there to carry it into the cells. If he's losing weight this could be happening to him too.
Please let us know what happens