EV3 with NiMH batteries
EDIT:

Yes, pressing the button will affect the indicator and low battery alarm/shutdown.

From the official LEGO firmware:

#define   BATT_INDICATOR_HIGH           7500          //!&lt; Battery indicator high [mV]
#define   BATT_INDICATOR_LOW            6200          //!&lt; Battery indicator low [mV]

#define   ACCU_INDICATOR_HIGH           7500          //!&lt; Rechargeable battery indicator high [mV]
#define   ACCU_INDICATOR_LOW            7100          //!&lt; Rechargeable battery indicator low [mV]

...

#define   LOW_VOLTAGE_SHUTDOWN_TIME     10000         //!&lt; Time from shutdown lower limit to shutdown [mS]

#define   BATT_WARNING_HIGH             6.2           //!&lt; Battery voltage warning upper limit [V]
#define   BATT_WARNING_LOW              5.5           //!&lt; Battery voltage warning lower limit [V]
#define   BATT_SHUTDOWN_HIGH            5.5           //!&lt; Battery voltage shutdown upper limit [V]
#define   BATT_SHUTDOWN_LOW             4.5           //!&lt; Battery voltage shutdown lower limit [V]

#define   ACCU_WARNING_HIGH             7.1           //!&lt; Rechargeable battery voltage warning upper limit [V]
#define   ACCU_WARNING_LOW              6.5           //!&lt; Rechargeable battery voltage warning lower limit [V]
#define   ACCU_SHUTDOWN_HIGH            6.5           //!&lt; Rechargeable battery voltage shutdown upper limit [V]
#define   ACCU_SHUTDOWN_LOW             6.0           //!&lt; Rechargeable battery voltage shutdown lower limit [V]


The BATT_* are used when the button is not pressed and the the ACCU_* values are used when the button is pressed.

ORIGINAL ANSWER:

The small black circle is used by the Li-ion battery pack from LEGO. This battery pack actually operates at a higher voltage that Alkaline batteries. On the other hand, NiMH batteries operate at a lower voltage than Alkaline, so pressing the small black circle would have the opposite effect of what you are hoping that it will do.