You don't need BT Broadband to run the app, just a working BT phone line. So I'd say the answer is No unless you're using it via your home wifi for some reason.
Its going to be a very tiny amount, as speech hardly uses any bandwidth, so I would not worry about it. Most of the time you will be using other connections anyway.
It possible that BT might be able to filter it out from the normal usage, as they do for Broadband Talk.
The reason I ask is that most of my use of it willbe on my home WIFI, & I'm monitoring our usage because of the suspected erroneous figures from December 2012.
We have inclusive anytime calls so once er indoors gets on the phone to her parents/mates it can be 59 minutes before she hangs up & then only to redial.
So I use the BBTalk to make outgoing calls but have to sit on the landing to use the phone wired into the hub, I never had any success getting the DECT to work on this HH2 😞
Now, with SmatTalk, I can be anywhere in the house & still dial landlines for free because of the package 🙂
if you are worried about the usage and are using a HH then just sign in to BTWIFI and then it will still be free and no usage on your account