two-port networks with voltage sources connected on ends
No, when you're measuring network parameters, you have to terminate the network correctly for the kind of parameter you're measuring.
Your \$T_{11}\$ parameter measures the voltage response at port 1 when the network is stimulated by a voltage at port 2. If you're measuring a voltage response, you need to terminate the response port with something that allows the voltage to vary freely. In the case of T-parameters, where current on port 1 is also a response parameter rather than a stimulus, you also need to allow the current to vary. That means terminating port 1 with a fixed impedance of some kind rather than with a source.
Similarly, when you measure Z parameters and you want to know \$Z_{21}\$ you're applying a current at port 1 as stimulus and getting voltage at port 2 as the response. Therefore you would (as the most convenient option, since you don't need to measure port 2 current and voltage simultaneously) leave port 2 open (aka terminate with a 0-A current source).