Not always. He should be safe if the normal pressure test revealed no puncture all the way through.
I have a spare tyre on my 4 x 4 that has a puncture rather close to the sidewall, which no tyre place wanted to fix.
It used to only go flat on me if I happened to park somewhere with that point of the tyre at the bottom where the normal bulge is, I could drive around for months with zero problems and then strike it unlucky.
I ended up plugging it myself. That was 16 000 km ago.