No. Pelican Products, Inc. is an independent company founded in 1976, headquartered in Torrance, California. They are famous for protective cases—camera cases, gun cases, drone cases, military/government cases, and consumer electronics cases (iPhone, iPad, laptop, console).
Pelican makes cases for consoles and controllers (e.g., "Pelican 1650 Case for PS5," "Pelican Vault for Switch"), but they are not a "video game accessory brand" in the sense of making controllers, headsets, or charging docks. They have no ownership ties to GameStop.
GameStop carries Pelican cases alongside other brands: PowerA, PDP, Hori, Turtle Beach, Razer, and first-party (Sony, Microsoft, Nintendo). Pelican is just one vendor in their accessories aisle.
Pelican = rugged cases for everything. GameStop = retailer. No corporate relationship.