Tunnel Identity will be unique between two peers of having GTP-U based interface. If eNodeB supports multiple IP addresses for data plane then TEID will be unique with the combination of one IP address. As such there is no relation of TEID uniqueness with the cell or UE.
There are number of things which considered by designing. So it depends where you are running the eNodeB software. If you are running eNodeB software in data center environment (cloud RAN), things will be different when eNodeB software runs in stand alone system.