The use of clarifying questions (CQs) is a fairly new and useful technique to aid systems in recognizing the intent, context, and preferences behind user queries. Yet, understanding the extent of the effect of CQs on user behavior and the ability to identify relevant information remains relatively unexplored. In this work, we conduct a large user study to understand the interaction of users with CQs in various quality categories, and the effect of CQ quality on user search performance in terms of finding relevant information, search behavior, and user satisfaction. Analysis of implicit interaction data and explicit user feedback demonstrates that high-quality CQs improve user performance and satisfaction. By contrast, low-And mid-quality CQs are harmful, and thus allowing the users to complete their tasks without CQ support may be preferred in this case. We also observe that user engagement, and therefore the need for CQ support, is affected by several factors, such as search result quality or perceived task difficulty. The findings of this study can help researchers and system designers realize why, when, and how users interact with CQs, leading to a better understanding and design of search clarification systems.