It absolutely can. Even if you're relying on wi-fi, the phone will still be trying to get a cell signal, as long as the radio is on. I encounter this at the hospital where I work -- terrible cell signal, and so my phone typically runs down much more quickly there than on any off day outside the hospital. I experimented with turning on Airplane Mode and then turning on wi-fi, since I could use wi-fi calling, and that did help with battery drain -- but the hospital's wi-fi network is also pretty bad, so I found myself dropping calls more often when I neared a wi-fi deadzone in the hospital.:-\