As conversational Text-to-Speech (TTS) technologies become increasingly realistic and expressive, understanding the impact of prosodic variation on speech perception and social dynamics is crucial for enhancing conversational systems. This study explores the influence of prosodic features on listener responses to indirect requests using a specifically designed conversational TTS engine capable of controlling prosody, and generating speech across three different speaker profiles: female, male, and gender-ambiguous. We conducted two experiments to analyse how naturalistic variations in speech rate and vocal energy (projection) impact the likelihood of request compliance and perceived politeness. In the first experiment, we examined how prosodic modifications affect the perception of politeness in permission- and service requests. In the second experiment participants compared pairs of spoken requests, each rendered with different prosodic features, and chose which they were more likely to grant. Results indicate that both faster speech rates and higher projection increased the willingness to comply, though the extent of this influence varied by speaker gender. Higher projection in service request increases the chance of being granted more than in permission requests. Politeness has a demonstrated positive impact on the likelihood of requests being granted, this effect is stronger for the male voice compared to female and gender-ambiguous voices.