This paper is motivated by a simple question: Can we design and build battery-free devices capable of machine learning and inference in underwater environments? An affirmative answer to this question would have significant implications for a new generation of underwater sensing and monitoring applications for environmental monitoring, scientific exploration, and climate/weather prediction. To answer this question, we explore the feasibility of bridging advances from the past decade in two fields: battery-free networking and low-power machine learning. Our exploration demonstrates that it is indeed possible to enable battery-free inference in underwater environments. We designed a device that can harvest energy from underwater sound, power up an ultra-low-power microcontroller and on-board sensor, perform local inference on sensed measurements using a lightweight Deep Neural Network, and communicate the inference result via backscatter to a receiver. We tested our prototype in an emulated marine bioacoustics application, demonstrating the potential to recognize underwater animal sounds without batteries. Through this exploration, we highlight the challenges and opportunities for making underwater battery-free inference and machine learning ubiquitous.