It is true that the Sheperd flight will pre-date Kennedy's pledge to go to the moon, but I don't think a suborbital flight is enough to cause America to sit on its laurels.
There were lots of opportunities for America to catch up the Russians and even beat them in the early space race. The Air Force was one bad Thor rocket away from getting a lunar orbiting probe in late 1958. But, the Soviets will stay in the Race so long as it's possible to beat the Americans in the end. They only gave up on the moon because they were so far behind.
The R-7 will launch people into orbit. The Redstone won't. Even if Gagarin's flight is delayed a few months, it will still bury the American accomplishment when it happens (just like Glenn's achievement dwarfed Sheperd's). And if America is at all complacent at any stage of the early space race, the Russians will just leapfrog ahead.
It's all academic, anyway. America let the Soviets dictate the pace of the American space program every step of the way. America waited for Sputnik to launch its first probe. Kennedy invented a missile gap to boost his ideas. In the late 60s, when it looked like America was going to beat the Soviets, we ignored those reports and focused on the possibility that the Soviets were still in the race. And when the Soviets finally threw in the towel, so did we.