Yes, the SimpleSENCE Leak and Freeze detector will work with a WiFi extender. We would recommend that you configure the sensor's WiFi at the location you wish to place your sensor. There are some WiFi extender/repeater implementations that actually create a second network. If that is the case, you will want to connect to the extended network segment.
For more information on WiFi connectivity check out our other article "How to optimize WiFi connectivity"