I would rather say a remote possibility. We should not forget that the "encircling" French and Anglo forces weren't the most powerful opponents either. Being unable to fight their way out in the situation given at the point would be rather hard to imagine.
But even if so....the Marne should the German readiness to react flexibly with a withdrawal towards shorter frontlines. If they move back towards the Ardennes, or even to the German frontier, they would have very short frontlines in defendable country - a beginning of the Trench war there would definitely forbid an end to the war within six weeks.
Also don't forget that the Germans were doing rather successfully on the front in Alsace-Lorraine. That is not half of the game, but still important.
And, I would like to add that other nations stayed in the game despite losing whole armies, i.e. Russia and Austria-Hungary.
Nevertheless, though, you are right. With an actual bloody defeat instead of a botched tactical maneuvre at the 1st Marne, the French and British would have quite an edge for the remainder of 1914, probably enabling them to hold on to substantially larger parts of Belgium and most if not all of Northern France.
But Germany would still have reserves. How much would they be weakened with the different Western Front? I cannot tell. Does it bring them to their senses at Christmas 1914? Probably not. In 15? 16? 17? Heck, maybe we have to wait until 1918 still.