I'm not sure it would. It's been a long time since I had access to Broadband Plus, so I'm not completely au fait with it now...but I am pretty sure it needs some sort of authentication, which I don't think an external box would provide. I may be wrong of course, and I am happy to be corrected.
You might have a look instead for something like a wireless speaker set-up. I've not heard the quality of anything like this, so you might need to do some searching for reviews etc, but a quick Google led me to these with a 100m range. Any good?
http://www.edirectory.co.uk/pf/880/mia/pid/1608025
EDIT: Or how about these for €1000
http://www.trustedreviews.com/periph...-Enthusiast/p1
EDIT 2: Here's a whole range of them for about the £100 a pair mark....again, can't vouch for the quality but they look nice !!!!
www.aqwirelessspeakers.com