Yes, passengers travelling in business class have access to Wi-Fi, though how much it will cost and how long a session will last depends on the type of plane and the Wi-Fi provider. On Boeing 777-300ER and 787-10, and on Airbus A350 and A380, business class passengers get one free Wi-Fi session up to 30MB. That’s plenty of data to put the “business” in business class and work on an email or presentation—or just to surf the web.