No, as I said, I've not had cause to run through this myself, but 98% sure that the initial interaction is just to register the account and receive a note of the DID & key.
Marginally simpler if you do it on the same PC because then you can just copy and paste the details, but I'm virtually certain that there's no interaction between your browser request for an account and the WL program. The WL version has not changed at all so the process with WL is just the same as it was previously when you received the details by email.
OK, I did the "install logger" process, and got my 12-character DID and 6-digit Key. Went to WeatherLink Setup, typed in those items, clicked the button to enter them and.... after a wait of a few seconds ....
Value Cannot be null
Parameter name: request UriString
Tried several times (cut-and-paste, typing, etc. etc.) with the same result. It's not sending data to my WeatherLink.com page. (Waited over an hour to be sure). But is still working OK with all other destinations.
I suppose it's time to send a question to Davis Support.
Footnote: it is obviously trying, In addition to the other things, the log file contains (once per minute)
12/25/17 3:31p (ValleyForge) Value cannot be null.
Parameter name: requestUriString
12/25/17 3:30p (ValleyForge) Value cannot be null.
Parameter name: requestUriString
Footnote 2: I'm running WeatherLink version 6.0.1 - is version 6.0.3 required to use WeatherLink.com this way?