Optimizing Retrieval-Augmented Generation (RAG) configurations for specific tasks is a complex and resource-intensive challenge. Motivated by this challenge, frameworks for RAG hyper-parameter optimization (HPO) have recently emerged, yet their effectiveness has not been rigorously benchmarked. To fill this gap, we present a comprehensive study involving five HPO algorithms over five datasets from diverse domains, including a newly curated real-world product documentation dataset. Our study explores the largest RAG HPO search space to date that includes full grid-search evaluations, and uses three evaluation metrics as optimization targets. Analysis of the results shows that RAG HPO can be done efficiently, either greedily or with random search, and that it significantly boosts RAG performance for all datasets. For greedy HPO approaches, we show that optimizing model selection first is preferable to the common practice of following the RAG pipeline order during optimization.