Speech disfluencies play a role in perspective-taking and audience design in human-human communication (HHC), but little is known about their impact in human-machine dialogue (HMD). In an online Namer-Matcher task, sixty-one participants interacted with a speech agent using either fluent or disfluent speech. Participants completed a partner-modelling questionnaire (PMQ) both before and after the task. Post-interaction evaluations indicated that participants perceived the disfluent agent as more competent, despite no significant differences in pre-task ratings. However, no notable differences were observed in assessments of conversational flexibility or human-likeness. Our findings also reveal evidence of egocentric and allocentric language production when participants interact with speech agents. Interaction with disfluent speech agents appears to increase egocentric communication in comparison to fluent agents. Although the wide credibility intervals mean this effect is not clear-cut. We discuss potential interpretations of this finding, focusing on how disfluencies may impact partner models and language production in HMD.