Query performance prediction (QPP) is a core task in information retrieval. The QPP task is to predict the retrieval quality of a search system for a query without relevance judgments. Research has shown the effectiveness and usefulness of QPP for ad-hoc search. Recent years have witnessed considerable progress in conversational search (CS). Effective QPP could help a CS system to decide an appropriate action to be taken at the next turn. Despite its potential, QPP for CS has been little studied. We address this research gap by reproducing and studying the effectiveness of existing QPP methods in the context of CS. While the task of passage retrieval remains the same in the two settings, a user query in CS depends on the conversational history, introducing novel QPP challenges. In particular, we seek to explore to what extent findings from QPP methods for ad-hoc search generalize to three CS settings: (i) estimating the retrieval quality of different query rewriting-based retrieval methods, (ii) estimating the retrieval quality of a conversational dense retrieval method, and (iii) estimating the retrieval quality for top ranks vs. deeper-ranked lists. Our findings can be summarized as follows: (i) supervised QPP methods distinctly outperform unsupervised counterparts only when a large-scale training set is available; (ii) point-wise supervised QPP methods outperform their list-wise counterparts in most cases; and (iii) retrieval score-based unsupervised QPP methods show high effectiveness in assessing the conversational dense retrieval method, ConvDR.