How long does the tea last? If it goes an hour, then maybe you could catch a 4:50 or so train. That would get you to the ticket counter about an hour before take-off. You'd have to hustle straight to your flight from there, assuming that there is no line to check in luggage. As soon as you arrive at the airport, inform someone at the airline about your soon departure and they could help you hurry through check in and security. Doable, especially if you're traveling solo. With a family? I wouldn't. The adrenaline rush of catching the flight would more than cancel the pleasure of the tea.