Large language models (LLM) have demonstrated remarkable capabilities in various biomedical natural language processing (NLP) tasks, leveraging the demonstration within the input context to adapt to new tasks. However, LLM is sensitive to the selection of demonstrations. To address the hallucination issue inherent in LLM, retrieval-augmented LLM (RAL) offers a solution by retrieving pertinent information from an established database. Nonetheless, existing research work lacks rigorous evaluation of the impact of retrieval-augmented large language models on different biomedical NLP tasks. This deficiency makes it challenging to ascertain the capabilities of RAL within the biomedical domain. Moreover, the outputs from RAL are affected by retrieving the unlabeled, counterfactual, or diverse knowledge that is not well studied in the biomedical domain. However, such knowledge is common in the real world. Finally, exploring the self-awareness ability is also crucial for the RAL system. So, in this paper, we systematically investigate the impact of RALs on 5 different biomedical tasks (triple extraction, link prediction, classification, question answering, and natural language inference). We analyze the performance of RALs in four fundamental abilities, including unlabeled robustness, counterfactual robustness, diverse robustness, and negative awareness. To this end, we proposed an evaluation framework to assess the RALs' performance on different biomedical NLP tasks and establish four different testbeds based on the aforementioned fundamental abilities. Then, we evaluate 3 representative LLMs with 3 different retrievers on 5 tasks over 9 datasets.