In mot cases a amp meter in series with the battery and the case at the tail cap end will show the current drawn from the cell , but if its a boost/buck driver the diode current may differ from the current measured from the cell .
Yes just remove the tail cap and use your DMM. The current from the batteries will always be different than the current to the diode, the most efficient driver is probably 92%. There's always some power dissipated as heat from the driver.