Not really. The Lusitania was heading into German infested waters. Wilson just need an excuse for the U.S. to enter WWI and the Lusitania was a convenient.
American entry into WWI is by no means inevitable.
The Lusitania had nothing to do with it. That sinking was ancient history by 1917.The decisive factors were the Zimmermann Telegram, and, immediately afterward, the sinkings of several American (not Britiah) merchantmen by u-boats.
Had Wilson wanted an excuse to go to war, there had already been plenty. By April 1917 the problem was finding a way not to. Had he been as uncompromisingly non-interventionist as Bryan, he could probably have blocked a declaration of war, but he was not, and neither were the majorities in both houses of Congress.