It is not a big enough factor.Might this not start a preventative 1910 war by Germany/AH/+ to try and win before it becomes impossible?
The Germans were expecting to win two decisive short campaigns (France and then Russia) followed by an admission of defeat and peace talks. Small arms logistic commonality is a signal of preparing for a long war, which voids one of the assumptions of the German plans.
The significant factor is the political will behind the common weapons idea, and that would not be preempted once existant.