My guess and my vote is no. The British may not need the Americans per say, certainly not to the same extent that they would in World War II, but in less than 150 years, the United States has gone from a colonial backwater to an emerging industrial superpower, and more importantly one that's on friendly terms with Britain. The British are increasingly concerned about a possible war with Germany, especially after 1905. They might be willing to act as a intermediary between the Americans and the Japanese, but the possibility of an alliance with the United States is going to become increasingly important to them and they're not about to risk that, certainly not over Japan.
Also if they did not take the US side WW1 would be very different.