Yes but it is minimal. A BlackBerry battery is about 1300mAH which means that the battery is capable of delivering 1 milli Amp (1/1000th of an amp) for 1300 hours.
The LED probably draws 5milli Amp (5/1000th of an amp) so running continuously the LED would run, on this battery for 1300 / 5 = 260 hours. The LED blinks for about 0.5 secs every 2 secs so it is on for only 25% of the time. This makes the LED draw effectively 5 x 0.25 = 1.25 milli Amps. This gives 1300 /1.25 = 1040 hours.
This example naturally ignores running the rest of the phone and the tiny circuit and CPU ticks required to run the LED.
The LED is using practically no power. Now consider that it only runs for 15 minutes so the duty cycle is actually 25% of my last number.
I neer keep the wireless network notification LED on. If I want to see if I have service I will just go to my lock screen. It's not like the inside of my pocket needs to know at all times.
The native LED doesn't drain really drain power in any significant manner. However, apps like BeBuzz can increase drain, depending on options chosen.
Correct, the LED itself uses little battery power.
It's the 3rd party apps like BeBuzz that run in the background that use more power. Again, the power drain of these apps could be minimal as well since I don't have a method of quantifying their power drain.