Of course, you can program a logic that controls the LEDs. As I already mentioned (see Rechargeable Lithium-ion Battery) the LED1, LED2 and LED3 are controlled by the device logic and therefore the state of them depends on the code you created. Only the “Power Good LED” and “Charge Status LED” are controlled by hardware and cannot be influenced by you.
You can find a lot of examples for controlling the LEDs of the rapidM2M Base Starter on Github (Basic Example_Collection. This example (11_Led_2.p) toggles LED2 every second and turns off all other LEDs.
If you rapidM2M Base Starter is running from the rechargeable battery it is advisable to reduce power consumption. You should not constantly turn on a LED. Also blinking where the LED is turned on and turned off for the same Time period is not the best idea if you want to save power. You should only turn on the LED for example 500ms (or shorter) and then turn it off for 30sec. You also can combine the button and the LED. So for example if the button is pressed the LED blinks for 5sec. and is then turned off until somebody presses the button again. For low power application it is advisable to turn off all LEDs if nobody is looking at them.
An Example for using the button can be found here: 10_Switch