Does Whatsapp require verification after Factory Reset?
Yes it will require verification, and you will need to be able to receive a text to verify your number with WhatsApp.  If your device/carrier has the ability to send/receive texts over wifi, that may be an option for you to verify your number.

Per WhatsApp's FAQ Page here:


  Requirements
  
  
  You can only verify a phone number you own.
  You must be able to receive phone calls and SMS to the phone number you are  trying to verify.
  You must have any call-blocking settings, apps or task killers disabled.
  You must have a working Internet connection through mobile data or Wi-Fi. If you are roaming or have a bad connection, verification may
  not work. Try opening www.whatsapp.com on your phone’s Internet
  browser to see if you are connected to the Internet.
  
  
  If you didn't receive the 6-digit code by SMS
  
  
  If the timer runs out before you receive the code, an option will appear to request a phone call. Choose the Call me option to request
  the call. When you answer the call, an automated voice should tell you
  the 6-digit code. Insert that to verify WhatsApp.