No mate, it doesn't have rechargeable battery pack as standard. It can be used with AA rechargeables though, but they don't allow so much headroom before the MFT may display random behaviour, particularly as ni-cad and ni-mh cells have a high self-discharge rate. Most users report better stability when using good quality (Duracell or Energiser) alkaline AAs.
Many users report random behaviour of the Fluke 165x series MFTs caused by low batteries. This is experienced in many cases well before the 'Low Battery' warning indicator is triggered at 6V and appears in the display. The accepted wisdom is to test the battery voltage before the MFT is used and if the battery voltage is below 6.5V, replace the set of batteries with new ones.
To test the battery voltage:
1) Turn the rotary switch to the V position.
2) Press F3 to initiate the battery test. The voltage display will clear and is replaced by the measured battery voltage in the secondary display for 2 seconds before returning to the normal voltage display mode.