In recent experiments at JET, a contribution to the neutron emission from reactions between beryllium and 3He, 4He and H has been identified. With the beryllium wall planned for ITER, this raises the question of possible neutron activation during the ITER zero-activation phase. Here, we estimate the neutron emission rates for various heating scenarios foreseen for this ITER phase using Monte Carlo simulations. The emission is seen to be strongly dependent on the scenario chosen and the assumptions involved. We find that fundamental minority heating can contribute on the scale of low temperature deuterium plasmas, depending on minority concentration and ion cyclotron resonance heating (ICRH) power applied. Harmonic ICRH leads to production of tails that can give rise to significant neutron emission rates, while rates from hydrogen beams will be near zero. Better knowledge of the zero-activation phase conditions, and more sophisticated ICRH codes, would be needed to give exact rate predictions. We conclude that rates from the so-called zero-activation plasmas will be significantly lower than expected for the DD or DT phases, but far from zero.