That seems unlikely. WiFi should certainly drain your battery less than cellular. (I have yet to jump on the smartphone train but my iPad gets consistent 7 hours with 3G, 10 hours with WiFi.)
I imagine it becomes most apparent if your device is polling for email. On every interval it needs to wake up, turn on WiFi, look for any available networks, discover there are none and then finally revert to the cellular network. With WiFi disabled, it can go straight to cell.
The iPhones were famously bad for this in the early days, though they seem to improve later on; either through a hardware or software update, I'm not sure which.
It appears that for newer devices, wifi uses a lot less power.