Conversational agents are playing an increasingly important role in providing users with natural communication environments, improving outcomes in a variety of domains in human-computer interaction. Crowdsourcing marketplaces are simultaneously flourishing, and it has never been easier to acquire large-scale human input from online workers. Recent works have revealed the potential of conversational interfaces in improving worker engagement and satisfaction. At the same time, worker moods have been shown to have significant effects on quality related outcomes. Little is known about the role of worker moods in shaping work in conversational microtask crowdsourcing. In this paper, we conducted a crowdsourcing study addressing 600 unique online workers, to investigate the role that worker moods play in conversational microtask crowdsourcing. We also explore whether suitable conversational styles of the agent can affect the performance of workers in different moods. Our results show that workers in a pleasant mood tend to produce significantly higher quality results (over 20%), exhibit greater engagement (an increase by around 19%) and report a lower cognitive load (by over 12%), and a suitable conversational style can have a significant impact on workers in different moods. Our findings advance the current understanding of conversational microtask crowdsourcing and have important implications on designing future conversational crowdsourcing systems.