Technically, this is a decision that the client-side LB policy makes. However, none of our policies currently create more than one connection per IP to send new RPCs. If you use long-lived RPCs, there could be old TCP connections with those old RPCs on them, but those connections will close when the RPCs complete.
The default LB policy is pick_first, which only has one "active" TCP connection independent of the number of IP addresses. round_robin has one active connection per IP.