A question worth asking though: Is it possible that in the event that the US does go into the war early, that US troops could be sent to the Russian Front to try and help stiffen up the Russian Army, either before or after the ousting of the Czar?
I can't see the Americans deploying in any great strength in Russia, as much for logistical reasons as anything else.
Let's look in more detail at the situation in which the AEF arrives. It's safe to assume that the AEF doesn't arrive any earlier or in any greater number, so the first divisions become combat ready in, say, May 1916, with army-sized formations combat ready by the fall. In the summer of 1916, the Entente would most likely want the Americans as part of the rotation strategy through Verdun, if anything. That would give the Americans one hell of an introduction (literally) to combat on the Western Front. By the late fall, you might see the Americans contributing to the last phases of the Somme, if Haig can be convinced to let some inexperienced Americans on his battle, or the Americans help push the Germans a bit further back at Verdun, but definitely nothing decisive (considering the state of tactics & technology on the Western in 1916, an extra million soldiers wouldn't make much of a difference).
So when Wilson goes up for re-election, he has practically nothing to show for the war but a long and growing casualty list, without any real indication that American intervention is actually contributing to victory. Would Wilson win re-election? Perhaps, though I would imagine there would be even more anti-war sentiment in the US ITTL than IOTL.
The first point at which I could see the Americans making a major difference might be if the addition of an American component to Nivelle's offensive makes him alter his plans sufficiently to not make them disastrous. More likely, the Americans just get slaughtered alongside the French at the Chemin des Dames - one of the great lessons of combat in 1915-17 was that adding more numbers to an attack just added to the death toll.
After the heavy losses of 1916, I could see the Americans trying to redeploy more on other Fronts, trying to find an easier way to defeat the Central Powers without the heavy casualties of the Western Front. Still, the Brits won't want them in the Middle East (they want the territory for themselves, after all), and the logistics were abysmal at Salonika at this time.
In the long run, I still think the Russians collapse in 1917. The end of the war might be accelerated by about six months or so - Germany would likely already be outnumbered in the spring of 1918, instead of having the window of opportunity they had IOTL, so the Entente might be attacking right from early 1918, with the benefit now of better tactics and technology.