Yes, Wifi looking for a hotspot will drain the phone. Also, being in a bad cell area will also drain the phone.
I use tasker toautomate turning wifi on and off so I don't need to think about it and so it's doesn't burn up battery life needlessly. It uses cell tower locations to determine when wifi should and should not be on.
For me, it turns wifi off when I leave for work in the morning (because my phone is no longer near certain cell towers near my house). It's off in the car. When I arrive at the office, it turns wifi back on (because it's near my work cell towers). I also have it set up to turn on near friends houses and my parents and places where I know I'll connect. The rest of the time it stays off and I simply don't need to think about it any more.
There are some youtube videos and if you google it you'll find instructions that will help you set it up.