Define "session".

As far as I know, applications running on the client machine that access services on the inside via VPN can't pick a special interface. This is done via the kernel routing table that after the creation of the VPN connection gets a new entry pointing at the virtual interface for all traffic in that subnet.

When it comes to established TCP/IP connections, any packet that's sent over the VPN connection has to be encrypted and sent to the receiver (client or server) using the normal connection. If this mapping were to break, I'd guess all established TCP/IP connections would be orphaned and removed by the connection tracking in the TCP/IP stack, possibly after some timeout.

If you only look at new connections, like clicking a new link in your browser, it might work even if you just reconnected the lower levels of the VPN system. But, to me, this is of limited use since that's not saving established connections.