Does turning on WiFi (without connecting to any wireless network) use battery?
Yes, turning on features will use more power. According to Apple, you can save power by turning off WiFi if you're not using that feature:
Optimize Your Settings
Depending on how they are configured, a few features may decrease your iPhone battery life. For example, the frequency with which you retrieve email and the number of email accounts you auto-check can both affect battery life. The tips below apply to an iPhone running iOS 5.0 or later and may help extend your battery life.
and more specifically:
Turn off Wi-Fi: If you rarely use Wi-Fi, you can turn it off to save power. Go to
Settings > Wi-Fiand set Wi-Fi to
Off. Note that if you frequently use your iPhone to browse the web, battery life may be improved by using Wi-Fi instead of cellular data networks.
The same principle is true for all other features (bluetooth, push email, etc.). Turn off what you don't need to conserve power.
Interestingly enough some people have found turning on WiFi to actually cause them to have better battery life. This is very much dependent on how you use it, but the people that I know who have experienced this say they are in strong wifi buildings with weak 3g signal. Having all of their email going over WiFi has saved them battery life.
But apart from that, all of the other guys are right, it will pull more power since you aren't actively connected but still pulling for networks.