Natural language interaction has evolved as a useful modality to help users explore and interact with their data during visual analysis. Little work has been done to explore how autocompletion can help with data discovery while helping users formulate analytical questions. We developed a system called Sneak Pique as a design probe to better understand the usefulness of autocompletion for visual analysis. We ran three Mechanical Turk studies to evaluate user preferences for various text- and visualization widget-based autocompletion design variants for helping with partial search queries. Our findings indicate that users found data previews to be useful in the suggestions. Widgets were preferred for previewing temporal, geospatial, and numerical data while text autocompletion was preferred for categorical and hierarchical data. We conducted an exploratory analysis of our system implementing this specific subset of preferred autocompletion variants. Our insights regarding the efficacy of these autocompletion suggestions can inform the future design of natural language interfaces supporting visual analysis.