The Engineers most certainly had line throwing capability on their AVRE tanks, even for firing demo charges. I wouldn't think that they'd use them to deliver tele cables per-se between trenches because for the line throwers to work, you have to use a new line each time that feeds from the centre of the bobbin. Otherwise a roll that's been re-wound by man WILL jamb up, believe me! I have no doubt that the Signals (the bleeps) and the Engineers would use rifle fired lines
Additionally of course, it's only a thin sisal (now nylon) line, about the dia of a pullthrough that it initally thrown and a large dia line is pulled over later. We had a sealed roll of man-capable line at Warminster used by the Commando's for rock/cliff scaling, thrown by a special 2" mortar bomb grappling hook affair. We used to rebuild the LT rifles from the small RASC and RN ships. What a mess they were.........