Charging NiMHs: about current fluctuation tolerance
Batteries are perfectly happy with intermittent charging current, whether Li or Ni based.

However, a charger that tries to be too clever, too smart, like your useless power bank one, may get confused by stop-start charging and do the wrong thing, or shut down, or fail safe.

Do not replace Li batteries with Ni ones in the same power bank module, that will totally confuse the charger, different voltage, different chemistry.

If you stay within the voltage and current limits for your battery, they will charge OK. 

Note that Ni based batteries will tolerate a steady overcharge. Li based batteries will not. That would make a considerable difference to the charger.