Text-to-SQL translates user queries into SQL statements that can retrieve relevant answers from relational databases. Recent approaches to Text-to-SQL rely on pre-trained language models that are computationally expensive and technically challenging to deploy in real-world applications that require real-time or on-device processing capabilities. In this paper, we perform a focused study on the feasibility of applying recent model compression techniques to sketch-based and sequence-to-sequence Text-to-SQL models. Our results reveal that sketch-based Text-to-SQL models generally have higher inference efficiency and respond better to model compression than sequence-to-sequence models, making them ideal for real-world deployments, especially in use cases with simple SQL statements.