Not at the Polynesian, they only have a bar. The bar might serve snacks (most likely prepackaged) but you'd have to ask if you can get them on the dining plan.
Captain Cooks is relatively near the pool.
Resort pools with CS meals on the plan are: Beach/Yacht Club (Hurricane Hannah's), Coronado Springs (Siestas Cantina), Contemporary (Sand Bar), Old Key West (Goods To Go).