From what I've read the Watch is linked to your EE mobile account its uses data and the same number as your phone
So I doubt it will work with BTMobile as they wont be able to add it
Copied from EE
4G Samsung Galaxy Watch – Launching exclusively on EE in the UK
EE will be the first UK network to support the 4G Samsung Galaxy Watch when it launches later this year. With the 4G Samsung Galaxy Watch, customers can take calls, receive messages and get notifications using the same number and data plan as their phone, while leaving their phone at home if they go out for a run or pop to the shops