F = ma so a = F/m. In the scenario you’ve set up m >>>>>> F, because the Earth is fucking enormous. So a will be extremely small but nonzero. A precise enough

F = ma so a = F/m. In the scenario you’ve set up m >>>>>> F, because the Earth is fucking enormous. So a will be extremely small but nonzero. A precise enough accelerometer would show you this. Also your mountain accelerometer would show ~9.8m/s^2 plus the extremely small contribution of the rocket thrust, not 0.