Building energy management (BEM) tasks require processing and learning from a variety of time-series data. Existing solutions rely on bespoke task- and data-specific models to perform these tasks, limiting their broader applicability. Inspired by the transformative success of Large Language Models (LLMs), Time-Series Foundation Models (TSFMs), trained on diverse datasets, have the potential to change this. Were TSFMs to achieve a level of generalizability across tasks and contexts akin to LLMs, they could fundamentally address the scalability challenges pervasive in BEM. To understand where they stand today, we evaluate TSFMs across four dimensions: (1) generalizability in zero-shot univariate forecasting, (2) forecasting with covariates for thermal behavior modeling, (3) zero-shot representation learning for classification tasks, and (4) robustness to performance metrics and varying operational conditions. Our results reveal that TSFMs exhibit \emph{limited} generalizability, performing only marginally better than statistical models on unseen datasets and modalities for univariate forecasting. Similarly, inclusion of covariates in TSFMs does not yield performance improvements, and their performance remains inferior to conventional models that utilize covariates. While TSFMs generate effective zero-shot representations for downstream classification tasks, they may remain inferior to statistical models in forecasting when statistical models perform test-time fitting. Moreover, TSFMs forecasting performance is sensitive to evaluation metrics, and they struggle in more complex building environments compared to statistical models. These findings underscore the need for targeted advancements in TSFM design, particularly their handling of covariates and incorporating context and temporal dynamics into prediction mechanisms, to develop more adaptable and scalable solutions for BEM.