This paper investigates how end-to-end (E2E) channel autoencoders (AEs) can achieve energy-efficient wideband communications by leveraging Walsh-Hadamard (WH) interleaved converters. WH interleaving enables high sampling rate analog-digital conversion with reduced power consumption using an analog WH transformation. We demonstrate that E2E-trained neural coded modulation can transparently adapt to the WH-transceiver hardware without requiring algorithmic redesign. Focusing on the short block length regime, we train WH-domain AEs and benchmark them against standard neural and conventional baselines, including 5G Polar codes. We quantify the system-level energy tradeoffs among baseband compute, channel signal-to-noise ratio (SNR), and analog converter power. Our analysis shows that the proposed WH-AE system can approach conventional Polar code SNR performance within 0.14dB while consuming comparable or lower system power. Compared to the best neural baseline, WH-AE achieves, on average, 29% higher energy efficiency (in bit/J) for the same reliability. These findings establish WH-domain learning as a viable path to energy-efficient, high-throughput wideband communications by explicitly balancing compute complexity, SNR, and analog power consumption.