Natural Language Processing (NLP) models based on Machine Learning (ML) are susceptible to adversarial attacks – malicious algorithms that imperceptibly modify input text to force models into making incorrect predictions. However, evaluations of these attacks ignore the property of imperceptibility or study it under limited settings. This entails that adversarial perturbations would not pass any human quality gate and do not represent real threats to human-checked NLP systems. To bypass this limitation and enable proper assessment (and later, improvement) of NLP model robustness, we have surveyed 378 human participants about the perceptibility of text adversarial examples produced by state-of-the-art methods. Our results underline that existing text attacks are impractical in real-world scenarios where humans are involved. This contrasts with previous smaller-scale human studies, which reported overly optimistic conclusions regarding attack success. Through our work, we hope to position human perceptibility as a first-class success criterion for text attacks, and provide guidance for research to build effective attack algorithms and, in turn, design appropriate defence mechanisms.