Machine learning (ML) models are successful with weather forecasting and have shown progress in climate simulations, yet leveraging them for useful climate predictions needs exploration. Here we show this feasibility using NeuralGCM, a hybrid ML-physics atmospheric model, for seasonal predictions of large-scale atmospheric variability and Northern Hemisphere tropical cyclone (TC) activity. Inspired by physical model studies, we simplify boundary conditions, assuming sea surface temperature (SST) and sea ice follow their climatological cycle but persist anomalies present at initialization. With such forcings, NeuralGCM simulates realistic atmospheric circulation and TC climatology patterns. Furthermore, this configuration yields useful seasonal predictions (July-November) for the tropical atmosphere and various TC activity metrics. Notably, the prediction skill for TC frequency in the North Atlantic and East Pacific basins is comparable to existing physical models. These findings highlight the promise of leveraging ML models with physical insights to model TC risks and deliver seamless weather-climate predictions.