Can glucose and insulin exist in the same container without reacting?
Glycoproteins come in O-linked and N-linked forms. For O-linked sugars, a glycosidic bond forms between the sugar and the hydroxyl of a serine or threonine side chain. For N-linked sugars, a glycosidic bond forms between the sugar and the amide of asparagine. The equilibrium for all these reactions lies on the side of hydrolysis in aqueous solution.


  Is it possible to make a reasonable prediction what would/not happen in the mixed glucose/insulin solution in the container?


Yes, in aqueous solution there is no expectation that a glycoprotein forms between insulin and glucose. In vivo, glycoproteins form in a coupled reaction involving the carbohydrate (usually an oligosaccharide rather than a single glucose), the protein and a nucleotide triphosphate.

However, if an individual has high blood sugar levels (i.e. high concentrations of glucose in the blood) for extended periods of time, hemoglobin (specifically, the N-terminal amino group and the sidechain amino group of lysine) will react with the sugar and become glycalated. This is used in the HbA1c diagnostic test for checking if someone has diabetes. After the sugar binds (reversibly), there is a further reaction (Amadori rearrangement) that leads to a long-lasting product.