Yes, you can register and apply for EE Weds tickets from any mobile. I've been using an O2 mobile for it for years. As you say, you are effectively registering your any-network mobile against your BB landline.
Whether the registration will work is a moot point. Since EE took it over the JOIN hasn't always worked and we had to call EE to register for it manually. Have you JOINed successfully by getting a affirmative text?
__________________________________________________________________________________________ If you think I helped please feel free to hit the "Star" button below. To phone EE: The local rate landline number 0207 362 0200 or Freephone 0800 079 8586 - Option 1 for Mobiles; Option 2 for 4G WiFi; Option 3 for Home Broadband & EE TV.
ISPs: 1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC = 2014: EE 20 Meg WBC