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Battery-free and intermittently powered devices offer long lifetimes and enable deployment in new applications and environments. Unfortunately, developing sophisticated inference-capable applications is still challenging due to the lack of platform support for more advanced (32-bit) microprocessors and specialized accelerators---which can execute data-intensive machine learning tasks, but add complexity across the stack when dealing with intermittent power. We present Protean to bridge the platform gap for inference-capable battery-free sensors. Designed for runtime scalability, meeting the dynamic range of energy harvesters with matching heterogeneous processing elements like neural network accelerators. We develop a modular "plug-and-play" hardware platform, SuperSensor, with a reconfigurable energy storage circuit that powers a 32-bit ARM-based microcontroller with a convolutional neural network accelerator. An adaptive task-based runtime system, Chameleon, provides intermittency-proof execution of machine learning tasks across heterogeneous processing elements. The runtime automatically scales and dispatches these tasks based on incoming energy, current state, and programmer annotations. A code generator, Metamorph, automates conversion of ML models to intermittent safe execution across heterogeneous compute elements. We evaluate Protean with audio and image workloads and demonstrate up to 666x improvement in inference energy efficiency by enabling usage of modern computational elements within intermittent computing. Further, Protean provides up to 166% higher throughput compared to non-adaptive baselines.