Does the gastroenteritis lead to upper respiratory infection?

Very rarely: Most of the microbes (i.e. Bacteria or viruses) which cause infectious gastroenteritis generally are only attracted to the gastrointestinal (GI) system. Therefore, it would be very unusual for a GI bacteria or virus to spread to the lungs. Occasionally patients with gastroenteritis aspirate (choke and cough) and develop an aspiration pneumonia. But this is a secondary problem.

Not exactly: Some viruses can cause both upper respiratory infections and gastroenteritis, but gastroenteritis rarely actually leads to upper respiratory infections.