With ongoing climate transformations, reliable Arctic sea ice forecasts are essential for understanding impacts on shipping, ecosystems, and climate teleconnections. This research examines physics-free neural architectures versus physics-informed statistical models for long-term Arctic projections by implementing Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN) alongside a seasonal SARIMAX time series model incorporating physical predictors including temperature anomalies and ice thickness. We test whether neural models trained on historical ice data can match physics-informed SARIMAX reliability, and whether approaches exhibit systematic biases toward specific emission pathways. Using data from January 1979 to December 2024, we conducted forecasts through 2100, with SARIMAX driven by CMIP6 sea ice thickness under SSP2-4.5 and SSP5-8.5 scenarios. Results decisively reject the first hypothesis: both neural models projected ice free Arctic summer by September 2089 regardless of emission scenario, while SARIMAX maintained physically plausible seasonal coverage throughout the century under both pathways. Neural approaches demonstrated systematic bias toward extreme warming exceeding even high-emission projections, revealing fundamental limitations in physics-free deep learning for climate forecasting where physical constraints are paramount.