Mr C.V. Woerd's patent was not for a new design of watchmakers' lathe, but special headstock where the opening and closing of collets was exclusively by a foot-operated, quick-action closer. From its appearance, the design would not have lent itself to be made with a draw-tube closer, the heavy spring, pivoting arm and various flanges, etc. precluding this--though I suppose the basic casting could have been used.
While foot-operated collet closers are occasionally found on larger bench precision lathes used for production work -  a more modern example being one fitted to a Japanese Eguro lathe - in nearly all cases this fitting will be an optional extra with much the same headstock also supplied with a draw-tube retainer or hand-operated holder. On lathes for watchmakers the writer cannot bring to mind any example of a headstock designed only with a quick closer, all being on the list of options and of the  direct-acting lever type, such as that found, for example, on the East German Georg Jacob, the German Wolf Jahn, the English Pultra, the American Derbyshire Magnus and Swiss favorite. If Charles Woerd managed to licience his invention, or go into production with it, is not known--but it does seem unlikely..