Recently, deep learning models have been widely applied in program understanding tasks, and these models achieve state-of-the-art results on many benchmark datasets. A major challenge of deep learning for program understanding is that the effectiveness of these approaches depends on the quality of their datasets, and these datasets often contain noisy data samples. A typical kind of noise in program understanding datasets is label noise, which means that the target outputs for some inputs are incorrect. Researchers have proposed various approaches to alleviate the negative impact of noisy labels, and formed a new research topic: noisy label learning (NLL). In this paper, we conduct an empirical study on the effectiveness of noisy label learning on deep learning for program understanding datasets. We evaluate various NLL approaches and deep learning models on three tasks: program classification, vulnerability detection, and code summarization. From the evaluation results, we come to the following findings: 1) small trained-from-scratch models are prone to label noises in program understanding, while large pre-trained models are highly robust against them. 2) NLL approaches significantly improve the program classification accuracies for small models on noisy training sets, but they only slightly benefit large pre-trained models in classification accuracies. 3) NLL can effectively detect synthetic noises in program understanding, but struggle in detecting real-world noises. We believe our findings can provide insights on the abilities of NLL in program understanding, and shed light on future works in tackling noises in software engineering datasets. We have released our code at https://github.com/jacobwwh/noise_SE.