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Wearable Cognitive Assistants (WCA) are anticipated to become a widely-used application class, in conjunction with emerging network infrastructures like 5G that incorporate edge computing capabilities. While prototypical studies of such applications exist today, the relationship between infrastructure service provisioning and its implication for WCA usability is largely unexplored despite the relevance that these applications have for future networks. This paper presents an experimental study assessing how WCA users react to varying end-to-end delays induced by the application pipeline or infrastructure. Participants interacted directly with an instrumented task-guidance WCA as delays were introduced into the system in a controllable fashion. System and task state were tracked in real time, and biometric data from wearable sensors on the participants were recorded. Our results show that periods of extended system delay cause users to correspondingly (and substantially) slow down in their guided task execution, an effect that persists for a time after the system returns to a more responsive state. Furthermore, the slow-down in task execution is correlated with a personality trait, neuroticism, associated with intolerance for time delays. We show that our results implicate impaired cognitive planning, as contrasted with resource depletion or emotional arousal, as the reason for slowed user task executions under system delay. The findings have several implications for the design and operation of WCA applications as well as computational and communication infrastructure, and additionally for the development of performance analysis tools for WCA.