Boncuk,
I have several rechargeable Nickel-metal hydride batteries. My workplace encourages us to use them as a gesture for the environment. They produce 1.2 volts when fully charged. If you want to allow the end user to use rechargeables, you couldn't use the voltage as an indicator of charge status. Really, the cell is depleted when it produces 0 volts. It is useless when the combined output is less than the requirements of your components (in this case, 1.8 volts total). Assuming the microcontroller and all other components still work acceptably at 1.8 volts, then that's all you need the cells to produce.
Richard