Measuring the propagation delay of a TDR pulse will not tell you anything about if the line is 50 ohm impedance or not. So the answer to your question is NO.
If he sends a TDR pulse down the line, and then looks for reflections (at the start of the line, further down the line, etc) and measures the MAGNITUDE of those reflections, then that will tell you if it is a 50 ohm line (the first big reflection) and if there are other problems (like reflections from via holes, bends, etc) further down the line.
Small TDR reflection amplitudes will also show up as a good return loss vs frequency on a VNA.