Well we have it now and a BT Cloud Phone (actually Yealink W60P and W53P base station and Dect phone).
The app' is reasonably good, but has a few problems: -
1. Hijacks SIM1 so calls appear in the phone log as arriving on a different connection.
2. Needs to be kept running, otherwise it misses calls.
Good points: -
1. Free [for now] voicemail.
2. Divert on no answer nearly seamless.
The cloud phone arrived unconfigured. Turns out the Yealink kit is very good supporting up to eight handsets and eight connections (compared to six and six on Siemens), however it took a long phone call and a complicated reset procedure to have it download its BT configuration. Doing so crippled the Yealink box, and locked it against local login, however it does what it says in BT' spec'.
To answer my own question, no you can't capture the registration parameters.
BT's earlier Voip products (Broadband Voice and Broadband Talk) used to send the registration parameters in the URL to set up their softphone(s).