If your existing service is overhead , then it probably makes no difference to the installer where the second line is to be provided ( within reason ) if the existing service is underground, then the external cable is at a fixed point and any new service would have to be wired from where the existing external cable attaches to, or enters the property....if your home office is a considerable distance from this point, and it would take a lot of time to run a cable to that location , the ‘engineer’ may not be to happy to do that amount of work on the type of job they have been given, having said that, BT offering a second line on the basis of making working from easier, you would think that ‘extra’ wiring would be expected , and BT were paying Openreach for the advanced line install and not just a basic install.
If ( for example ) your home office was in a detached ‘shed’ at the bottom of the garden , then I doubt you would get a line installed there under this ‘offer’
