This depends on the internal resistance of the battery and the resistance of the load. The current has nothing to do with the capacity rating (e.g. 2000mAh). The rating means that a 2000mAh battery can deliver 2000mA for 1h (as an ideal battery without losses).
Depending on the battery type it is possible to get a roughly charge level by measuring the voltage. For example this is possible for lead-acid (Pb) or Li-Ion batteries, but not for NiCd or NiMH. Note, that during the measuring the battery has to be connected to an electrical load, because the idle voltage is in general higher.
BK-3MCDE AA or BK-4MCDE AAA (2000 cycles, Made in Japan)HR-3UTC / HR-3UTG AA or HR-4UTC / HR-4UTG AAA (2000 cycles, Made in Japan)GP210AAHCB AA or GP85AAAHCB AAA (1500 cycles)