There's good reason to believe the Germans did not expect a two-front war, especially as the mood in the U.S. was decidedly non-interventionist until the Japanese attack on Pearl Harbor on 7 December 1941. Until the American entry, the British strategy had fallen to using their navy to forestall a possible invasion of their own homeland while fighting to preserve the distant colonies from which they drew the bulk of their war resources.

If any "tacit agreements" were made, it was more likely with the aim of avoiding further rousing the British fighting spirit and encouraging them to withdraw from the war while they still had their empire largely intact. Most likely, the Germans believed the Americans would sit out the war, since the Americans had done little except send arms and destroyers to the Brits in the year between the conquest of France and the invasion of Russia, and with British forces tied down both in Africa and holding territory the Japanese had their eyes on, the odds of a British surge across the Channel were remote to the point of being non-existent. Historical records showed that the Reich tended to be positively disposed toward the British, considering them to be more closely on a par with the Aryan race - if anyone could be - and therefore did not pursue the war as aggressively against them as the Reich later did against the Russians. If there is any doubt about this, one need only look toward the treatment of British verses Soviet POWs by the Reich.

The real question here is: had the Japanese not attacked Pearl Harbor and triggered U.S. intervention at that point, would the Russians have won WW-II and occupied Europe? German forces committed to halt the Allied advance in Italy could have instead been committed to the war against Russia, but it was pretty clear after the August 1943 Battle of Kursk that Germany was on the defensive in the East. The 1943 Africa campaign and subsequent invasion of Sicily and Italy depended heavily on American forces - the Brits alone could never have pulled it off, and they certainly could not have pulled off a D-day alone. Or, with continued American dithering, the prospect of a Russian occupation of Europe and Churchill's well-known antipathy for the Soviets, would the Brits have settled their differences with the Germans and then turned to supplying them in an effort to halt the Russian advance?

As to the Brits being "spared annihilation" - perhaps, or perhaps Hitler put too much faith in his Luftwaffe's claims that they could prevent an evacuation of Dunkirk (though they did rack up an impressive score of British ships sunk), or perhaps he made the pragmatic decision to press and defeat the French rather than let them regroup while he depleted his forces eliminating the Dunkirk pocket. As of June 3, when the Dunkirk rearguard was finally overwhelmed, the French Maginot Line remained intact and the Germans were trying to push through a defensive line that ran along the Somme and Aisne rivers to the Maginot defenses, with roughly 50 miles to go to reach Paris. It turned out that the French were depleted and that the Dunkirk evacuation gave the Brits the will to continue the war, but the Germans at the time could not have known that and might have feared a resurgent French defense of Paris turning into another long war of attrition.