While I can't unequivocally say that the horse casualties of the war (and the equine riders and trainers and stable hands beside) did or did not affect the rise of automobiles, I can say for certain that they by no means created the idea of an automotive industry or even the mass public use of automobiles, both of which was well established even early on in the war.

Famously, the ["Marne Taxi"] (https://en.wikipedia.org/wiki/Renault_Taxi_de_la_Marne) was used in the First Battle of the Marne, requisitioned by French forces to assist in the mass movement of French troops to shift positions to face the German push for Paris and shore up the line. While their use in that battle is somewhat overplayed, it does go to show you that the French had automobile taxis, and had them in such numbers that they provided a memorable and appreciable difference in the battle.

In the US, Fred H Colvin's "Sixty Years with Men and Machines" states that as of 1917, there was 127 different makers of just American automobiles. he likens the trend to that of early locomotive engineering where the same happened: at the beginning everyone wanted a piece of a new and exciting industry, and within ten or twenty years it got brought down to a mere ten or twenty major producers instead.

What all this implies again however, is that the Automotive trade was alive and well, and indeed showing a bit of a creative, if not industrial or financial, golden age before, and even during World War I.