Is this feasible?

I agree with Robin2, some things about this design do not make sense. WiFi can generally cover an area of at most a radius of perhaps 100m. Why would you need so many rain sensors in such a small area? Why might they give different readings to each other?

If you definitely want to stick with WiFi, then keep things simple by using a WiFi capable "Arduino" such as NodeMCU or Wemos Mini (or mini pro which has a socket for an external WiFi antenna). These devices have lots of flash memory to store data if the WiFi router is down. The problems that these boards bring is that they are not low power, so running on batteries can bring difficulties, and they have few pins, so more external chips will be needed to interface with the sensors. I would consider i2c I/O expanders and i2c ADC chips or boards.