It's more complicated than a simple yes or no. When the Germans declared unrestricted submarine warfare in February 1917, the British saw a sharp rise in tonnage lost to German U-boats. Had the tonnage lost continued to remain as high as it was at the peak of the U-boat campaign, it may have caused shortages of food and materiel in Britain, the industrial heart of the Allied war effort. Combined with the one-two punch of knocking the Russians out of the war, Germany may have been able to force the British and the French into an armistice on favourable terms.

However, the sharp drop in tonnage sunk shortly after the first few months of USW had nothing to deal with American intervention, but rather British innovation (or perhaps, dusting off a version of a very old tactic). After the initial sharp losses, the British began forming convoys with their transport. Previously, the British Admiralty had thought that convoys would provide minimum protection while increasing the size of targets, and stretching limited naval resources in risky, unglamorous missions. The plan was reformulated and trialed in 1917, and proved to be a sufficient deterrent, hence the drop.

That being said, the question of the Battle of the Atlantic was not decided in favour of the defender just yet, and in the second round in 1940-41, German wolfpacks (essentially grouping up submarines the same way the British grouped up convoys) did cause havoc, but the First World War ended before Germany could come up with a counter-countermeasure, in part because of failures on the Western Front to win decisive battles during the Spring Offensives, in which the America played a small but crucial role. In short, no, unrestricted submarine warfare could not have ended the war without continuing innovation to match British changes in tactics, but American involvement meant that the timeline was shortened to the point that Germany could not come up with the next military technology.