According to Icy-veins.com you are Able to log into the game with your Phone Number.
The 8.2.5 PTR login screen has been updated with the option to log into the game with your phone, instead of just mail. The function hasn’t been tested on PTR yet, but we found a global string which was recently changed in 8.2.5. The “Blizzard Account Name” field is now called “Email or Phone”.
Blizzard Account NamEmail or Phone