More than that. If your insulin levels are high, your pancreas won't even release glucagon. You need both glucagon and insulin and your body produces both in a delicate balancing act. When blood sugars are high, pancreas releases stored insulin (phase 1 response) when you first start eating. If your blood sugar is still rising after 45-60 minutes, the phase 2 insulin response kicks in where your pancreas starts producing more insulin to get the blood sugar out of the blood stream and into the cells where it can be used for energy. When blood sugar drops and there are no more carbs/sugar coming in, insulin production stops and the pancreas releases glucagon which stimulates the liver to release it's glygogen stores or make more glycogen through coverting amino acids. In this way, the body maintains a steady blood glucose.
We run into problems when the balance is disrupted (too much insulin).