Coarse-grained water models are ~100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with all-atom TIP4P/2005 and TIP4/Ice. These all-atom models were parameterized using high-pressure experimental data, and are either accurate for water’s EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parameter-ized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from com-pression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduce the temperature, enthalpy, entropy and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with accuracy that rivals both TIP4P/2005 and TIP4P/Ice. We interpret that the accu-racy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temper-ature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pres-sure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibil-ity of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it prom-ising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.