Is it possible to switch off wifi, and what current does it draw without wifi?
Yes definitely, you can easily switch off the wifi. On my bench an Omega2 draws 190mA with wifi on and 120mA with the wifi turned off.
Here are several ways to disable wifi -
During a session - in a terminal window the command "wifi down" turns off the wifi and "wifi" or "wifi up" turns it back on. Documented here near page bottom.
First I'll state the obvious... you will have a UART or appropriate dock for serial connection before testing this. By modifying the wireless config file, as mentioned here the Omega will turn off wifi while starting up.
You can toggle wifi off/on via a push button or a timer and the scripts, as detailed in those LEDE instructions. (edit - here the code tied to the "SES" button would be changed to work with input from a push-button on an Omega GPIO pin.)