Yes, but it takes a while.
Most manufacturer's recommend using powdered milk (also known as dried milk) within 18 months, but this is really just a "best by" date. According to the USDA, powdered milk can be stored indefinitely. To maximize the shelf-life, store your powdered milk in a dry environment or consider freezing it.
If ultra long-term storage is your goal, opt for non-fat powdered milk. It's much more shelf-stable than whole milk varieties.
How to Tell When It's Time to Toss It
Discard any powdered milk that develops an off odor or yellow coloration. These are signs that the milk has finally gone bad.