The answer is – it depends on the test results.
A weak (low) emission tube will last shorter time than a strong one. But you may not hear the difference when both tubes are within operating range. When a tube emission gets too low, the tube as part of the circuit is no longer operating at the optimal condition and will cause distortion in sound. It may also stress other parts of your amp causing equipment failure.
Noise / micro phonics issue on a preamplifier tube can be heard. Micro phonic is common on large power tubes but it is not important for sound quality.
Heater-to-Cathode leakage cannot be heard, but it will kill the tube faster before you know it.
Excessive gas will certainly shorten the tube life – but you cannot hear it.
A set of tubes with bad matching may cause distortion in some cases and become audible.
Do you need perfectly tested and matched tubes? Not always. You have to find the balance point yourself. Not everyone is perfectionist, but a seller should make all information known to let the buyer to make informative decision.