Not being able to get replies back would mean that setting up a new TCP connection would be impossible because you're not getting replies to the initial handsha

Not being able to get replies back would mean that setting up a new TCP connection would be impossible because you're not getting replies to the initial handshake. The TCP connections that were alive when the routes were dropped would time out pretty quickly if they weren't getting any replies. Whether UDP packets could get out is going to be down to how the connectivity was dropped. If it's just via BGP then there's a chance.