Incomplete data is a crucial challenge to data exploration, analytics, and visualization recommendation. Incomplete data would distort the analysis and reduce the benefits of any data-driven approach leading to poor and misleading recommendations. Several data imputation methods have been introduced to handle the incomplete data challenge. However, it is well-known that those methods cannot fully solve the incomplete data problem, but they are rather a mitigating solution that allows for improving the quality of the results provided by the different analytics operating on incomplete data. Hence, in the absence of a robust and accurate solution for the incomplete data problem, it is important to study the impact of incomplete data on different visual analytics, and how those visual analytics are affected by the incomplete data problem. In this paper, we conduct a study to observe the interplay between incomplete data and recommended visual analytics, under a combination of different conditions including: (1) the distribution of incomplete data, (2) the adopted data imputation methods, (3) the types of insights revealed by recommended visualizations, and (4) the quality measures used for assessing the goodness of recommendations.