Yes, the Zimmermann Note, along with the Germans re-instating unrestricted U-boat warfare just prior to the Zimmermann Note being made public, caused U.S. entry into WWI.
I mean the works of military historian Barbara Tuchman on the WWI era are the best starting resource. Her's is the most comprehensive coverage, although I will give the final summary in the last paragraph here.
Barbara Tuchman's books on this issue, in the order I suggest they be read:
Now to the summary: The USA could not have avoided getting involved in WWI! That's as hard a fact as that of water being wet.