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As voice-based assistants such as Alexa, Siri, and Google Assistant become ubiquitous, users increasingly expect to maintain natural and informative conversations with such systems. However, for an open-domain conversational system to be coherent and engaging, it must be able to maintain the user's interest for extended periods, without sounding boring or annoying. In this paper, we investigate one natural approach to this problem, of modulating response prosody, i.e., changing the pitch and cadence of the response to indicate delight, sadness or other common emotions, as well as using pre-recorded interjections. Intuitively, this approach should improve the naturalness of the conversation, but attempts to quantify the effects of prosodic modulation on user satisfaction and engagement remain challenging. To accomplish this, we report results obtained from a large-scale empirical study that measures the effects of prosodic modulation on user behavior and engagement across multiple conversation domains, both immediately after each turn, and at the overall conversation level. Our results indicate that the prosody modulation significantly increases both immediate and overall user satisfaction. However, since the effects vary across different domains, we verify that prosody modulations do not substitute for coherent, informative content of the responses. Together, our results provide useful tools and insights for improving the naturalness of responses in conversational systems.