The other other reference I find to them using the Telescoped 1903 besides the Cup, pre WWI, was they were a training tool. And this is probably the primary purpose of them honestly. It makes the most sense. The interviews I have read, said they could put them in the hands of a team shooter, and looking through the telescope at long distances, it would help them control holding the rifle more steady. They said looking through the magnification it was easier to see how little movements effected your shot at a 1000 yards. And it sounds like they were used for snapping in. As they practiced trigger pull looking through the scope, to see how trigger pull affected the movement of the crosshairs on the target. So it honestly sounds like they might not have been shot that much. But I've found several mentions of them doing this in 1916 and before, and even a mention in 1913. In 1919, when the teams reformed, they continued the practice. In fact in 1919, they detail that they have (40) of these telescoped 1903's set up to train on holding the rifle steady, that were available to the rifle team. I have not yet found a reference to how many they had pre WWI.
But yeah that is the most I can come up with so far on them using them pre WWI. But I will keep digging, but from everything I have read so far, it just sounds like they had the scoped rifles almost as soon as they switched form the Krag to the Springfield in competitions in 1908/09.