Semi-supervised learning (SSL) offers the potential to improve predictive performance by exploiting unlabeled data alongside limited labeled examples. While SSL has demonstrated success in many applications, it is not guaranteed to outperform traditional supervised learning and can, in some cases, achieve worse predictive performance. The success of SSL methods relies on certain assumptions about the relationship between the descriptive attributes and corresponding labels, such as low-density separation and smoothness assumptions. Despite the risk of performance degradation, the conditions under which SSL performs well (including the validity of SSL assumptions in real-world data) are poorly understood and seldom investigated. In this study, we investigate the viability of semi-supervised learning for mitotic phase classification using Raman spectroscopy data. Determining the mitotic phase of a cell has numerous important applications in biology, medicine, and other fields. This task is also particularly well-suited for semi-supervised learning, as obtaining labels involves laborious analysis of microscopy images by experts. We evaluate two SSL approaches: semi-supervised predictive clustering trees (SSL-PCTs) and semi-supervised masked autoencoders, and compare their performance against supervised baselines across varying amounts of labeled data. Our initial findings indicate that these methods generally fail to outperform supervised methods. We assess the low-density separation and smoothness assumptions using inter- and intra-class distances and local class homogeneity, finding that our spectroscopy data mostly violate these assumptions. In experiments limited to biologically distinct mitotic phases that comply with SSL assumptions, SSL-PCTs outperformed supervised ones, demonstrating the critical role of data structure in determining the success of semi-supervised methods.