The chance for America joining Germany were slight in 1914 and almost impossible in 1917.
Keep in mind that Wilson was reelected in November 1916, inaugurated in March 1917, and we were at war by April 1917. I think he was holding out for reelection on the peace bid and then as soon as he got it, jumped in.
Remember, if we gave billions to the Allies in loans, we damn well hoped to get our money back plus interest. Even if Wilson wasn't an Anglophile, which he was, he still would've had the bankers breathing down his neck... and not to mention a very tricky policy towards submarines.
But could America have sided with Germany if we make the point of divergence a little further back? Let's go back to 1896. In 1896, the United States and Great Britain almost went to war over a stretch of the Orinoco River in Venezuela because of a border dispute between British Guinea and Venezuela.
Had this happened, it is likely that the war would have ended in a stalemate, the United States winning a land war against Canada but greatly losing the naval one. This would have been at the ideal time as well since Alfred Thayer Mahan was making his arguments for an improved navy. As history has shown the loser is often the one who makes the most changes to military policy, and so the U.S. probably would have begun a build up of naval power even greater than what they did in reality.
But McKinley (who was opposed to the the Spanish-American War) would have probably been able to avoid the confrontation with Spain in 1898 since the USA had just gotten out of the war... and besides the major pretext, the
Maine incident, likely would have never happened.
The 1896 naval war also would have likely involved submarines, which would have been their first real use in action, and as a result, they likely would've received greater attention when the international policy on naval warfare conduct was written up in 1900? i think.... Basically, the international policy said that a vessel had to signal to a ship that it was going to fire upon it beforehand so that it would give a chance for people to evacuate... of course, that makes a submarine rather useless since the element of surprise is its greatest strength.
It is also likely that the war may have sent a shockwave through the political arena of American history for the next decade, and it's possible that McKinley might not have been shot at all. If this were the case, it would be up to Teddy Roosevelt to distinguish himself and get elected on his own, which would've taken at least another four years and possibly another eight. In which case, he would have likely run against Wilson in 1912 and won because it was a combination of his insistence that he would not seek a third term and his choice to go with the Progressive Party rather than the Republicans that cost him the election in the real timeline.
With a country still cool towards Britain after the 1896 war, and with a President who openly declared in 1896 that we should invade Canada, it is possible that the situation would have been different. The bankers and the President might have thrown their support beyond the obvious up-and-coming power in Europe: Germany, and the situation would have been entirely reversed. Plus, Britain's flagrant disregard for international policy by mining the North Sea would have given even greater cause to the Americans.
But the real issue is the money. Whoever the bankers back is ultimately going to determine which side the USA comes in on. In fact, it is also possible that fearing American support for Germany, Britain may have decided to stay the hell out of the continental war altogether in 1914. It almost happened anyway in real life.
Just some thoughts... long-winded though it may be