arXiv:2602.00851v4 Announce Type: replace-cross Abstract: AI agents combine normal conversation with autonomous task execution, allowing earlier context to shape how later tasks are executed. Yet studying this possibility is challenging because agent behavior is noisy and costly to reproduce, and observed behavioral changes can be difficult to separate from generic context sensitivity. We first ask whether task-irrelevant persuasion changes how agents act, a phenomenon we call \emph{persuasion propagation}, and whether persuasion susceptibility explains variation in these effects. We show that persuasive interaction leaves a measurable, task-dependent behavioral footprint on downstream agent execution. In web research, it increases execution time by 56\% and domains visited by 16.3\% relative to a baseline, while coding shows faster execution with larger revisions. However, agents that are more susceptible to persuasive conversational context do not reliably predict the magnitude of the downstream behavioral shifts. This motivates behavior-level evaluation of persuasion in AI agents.