Yes it definitely does as the broadcasting signal pumps up juice to keep the wireless working. As for how much, I am not sure. Some claim that it drains the battery pretty fast but it may be some kind of glitch in their case though I cannot be sure. I only turn on the Wi Fi to update my reader, check on new stuff online then I turn it off.
What other needs could you have to keep it on at all times ?
I suggest you turn it off when reading.
