These days, young people report to be in a state of permanent alertness due to their smartphones. This state has been defined as smartphone vigilance, an awareness that one can always get connected to others in combination with a permanent readiness to respond to incoming smartphone notifications. We argue that receiving a notification makes users vigilant and activates goals (e.g., checking the message) that interfere with other goals needed to perform a task. We thus hypothesized that smartphone vigilance impairs maintenance of current task-goals in working memory, resulting in increased goal-neglect. To test this hypothesis, we conducted a preregistered experiment that examined the effect of smartphone vigilance (incoming notifications) on goal-neglect in a modified Stroop task. We found evidence that participants perceived notifications as distracting, but vigilance did not lead to increased goal-neglect. To the contrary, there was tentative evidence that vigilant participants performed better at the task.