Unrestricted submarine warfare is not something the US can ignore. American ships were sunk, American lives were lost. Sure, the DoW might come a month or so later without Zimmerman's, but it would come.
True, but that could have been a while.
After the sinking of the Aztec on April 1 there was no further American loss of life until April 28 when the Vacuum was torpedoed, and then no more until the sinking of the Rockingham on May 16. All other sinkings in this period followed "cruiser rules" and caused no casualties. So if the Vigilancia and Aztec sinkings had not suffice to make up Wilson's mind, it could be well into May before he did so. It is one of the oddities of the whole "USW" caper that Germany accepted war with the US for quite literally the right to sink an additional two or three ships, some even of which might have been sinkable by cruiser rules if the U-boat captains had been so minded.
Most likely the sinkings would still have led to war at some point. But with Wilson one never knows. Had h still been neutral in early May, he would probably have been aware of the enormous rate at which British ships were going down. Herbert Hoover recalled that on his return to America, his ship heard numerous distress signal from sinking vessels, but dared not respond for fear of herself attracting the attention of a U-boat. It also passed within fifty feet of two mines. In such circs, Wilson might have come to think (erroneously but he mightn't know that) that entering the war was futile because American troopships would just get sunk on the way. Probably not, but you never can tell. He's a hard guy to read.