It's possible George but Cox's was the largest factory in Britain when built and was completely self sufficient. There were other works which did preparation of the jute fibre, these were the mills. There were also works which took the prepared thread, weft and warp, and wove it into cloth, these were spinning sheds or factories. To accuse a weaver of working in a mill was an intolerable insult.
The cloth went to a calendar for finishing. Cox's imported jute from present day Bangladesh and produced the multitude of finished and semi-finished goods. It had its own calendar and dyehouse. It may be of interest that fuse for explosives was made from jute so sandbags were not the only war material made in the jute works. Of course in the pre-synthetic days, jute was made into packaging for everything from coal to sugar and flour. Most of the sacks unloaded at the stores in France & Flanders would have been made in Dundee. Another product of Dundee textile works was canvas, made from flax rather than jute. Awnings, gun covers etc. would have left Dundee in the form of bolts of canvas heading for the people who made the finished articles. Strong connections here with Belfast where the finer flax products were made, i.e. linen. Sharing the docks and harbour area where the jute was unloaded was the main submarine base for the North Sea.