time domain reflectometer determining impedance
When using a signal generator with a known resistance (impedance) we
should be able to calculate the impedance of any cable by the
amplitudes of the reflections. Is my assumption correct?

It's a little bit easier than that - you don't need to wait for the reflection; at the point you apply the signal (50 Ω source), it is the voltage instantly developed at the cable that determines the impedance. For instance, if your pulse is 1 volt and has a source impedance of 50 Ω and, it connects to a 100 Ω cable, the voltage seen at the cable is: -
$$V_{CABLE} = 1\text{ volt}\cdot \dfrac{100}{100 + 50} = 0.6667\text{ volts}$$
If the cable were 50 Ω impedance then the peak voltage is 0.5 volts.