No, the main aim of the Zimmerman telegram wasn't to bring the US into WW1. It was intended as insurance against the likelihood that the US would join WW1 anyway over Germany's resumption of unrestricted submarine warfare.

This is the full text of the Zimmerman telegram, sent from the German foreign ministry to the German ambassador to Mexico. English translation, obviously, and the emphasis is mine.

We intend to begin on the first of February unrestricted submarine warfare. We shall endeavor in spite of this to keep the United States of America neutral. In the event of this not succeeding, we make Mexico a proposal of alliance on the following basis: make war together, make peace together, generous financial support and an understanding on our part that Mexico is to reconquer the lost territory in Texas, New Mexico, and Arizona. The settlement in detail is left to you. You will inform the President of the above most secretly as soon as the outbreak of war with the United States of America is certain, and add the suggestion that he should, on his own initiative, invite Japan to immediate adherence and at the same time mediate between Japan and ourselves. Please call the President's attention to the fact that the ruthless employment of our submarines now offers the prospect of compelling England in a few months to make peace.
Signed, ZIMMERMANN

Germany had decided to resume Unrestricted Submarine Warfare (USW) in 1917 for two reasons, one military and one domestic political. USW means that submarines may sink any merchant ships in the declared exclusion area, regardless of national flag, and without warning. As opposed to the "Prize Rules" or "Cruiser Rules" traditional international law had applied to commerce raiding, where only enemy-flagged merchant ships were legitimate targets. Ships belonging to neutral countries could be stopped and searched, and seized or sunk if they were found to be carrying contraband to blockaded ports or if they tried to resist the search, but could not be summarily attacked. Any ships to be sunk under cruiser rules must first be given reasonable warning for the passengers crew to abandon ship. These rules were developed with surface warships (particularly frigates and cruisers) in mind, not submarines, and submarines of the era didn't have anywhere near enough crew to search and seize a merchant ship, and submarines relied on stealth to be effective combatants so surfacing and summoning a merchant ship to submit to search or ordering the crew to abandon ship was risky, especially after the British started disguising armed merchantmen as ordinary merchant vessels in order to sink German subs when they surfaced (this was legal under international law as long as the disguised ship revealed its true nature by raising a Navy flag before opening fire).

Germany had previously attempted USW briefly in 1915, only to call it off after the US responded to the sinking of the Lusitania (a British ship sailing from New York and carrying many American and British passengers as well as a cargo that included war materiel being imported by Britain). The sinking was done without warning by a submerged U-Boat, the British denied the presence of war materiel on the ship (and the Germans had no hard evidence to the contrary), and 128 Americans (along with over a thousand British and other nationalities of passengers and crew) died. The US responded with vigorous diplomatic protests, stopping about half a step short of threatening war if USW continued. Germany acquiesced at the time and resumed cruiser rules.

The military reason was that the German navy had overestimated the effectiveness of USW and underestimated the British and American ability to build new merchant ships to replace those sunk. Based on their mistaken assessments, the Germans believed that they could sink enough merchant ships to prevent Britain from importing the food and raw materials they needed to continue the war, and that this would happen before Americans could mobilize enough to have a significant effect on the war.

The domestic political reason was as a response to the British blockade of Germany. Britain had been blockading Germany (with surface ships, operating under cruiser rules) since the outbreak of war, and Britain had been taking a very broad basis for what constituted war materiel. Specifically, food and fertilizer were counted as contraband, since food could be sent to the front to feed soldiers, and since fertilizer could be remanufactured into explosives. Germany had imported a large portion of its food pre-war, and German civilians had been on short rations for much of the war. The Winter of 1916-1917 (called the "Turnip Winter") was a period of particular hardship for German civilians, as the 1916 potato crop had failed, compounding the food shortage. Unrestricted Submarine Warfare was seen as a way for the German Navy to demonstrate to German civilians that they were Doing Something about the blockade and inflicting the same kinds of hardship on British civilians that the British Navy was inflicting on German civilians.

Once the decision to resume USW had been made, war with the US was considered inevitable. The idea of the Zimmerman Telegram was to exploit Mexican grievances against the US (not just the lost territory from the 1846-48 US/Mexican War, but also the much more recent US punitive expedition expedition in pursuit of Pancho Villa) to bring another country into the war on the German side as counterweight to the US joining the Entente. Every division the US Army used to fight Mexico was a division that couldn't be sent to France to reinforce the British and French armies, so forcing the US to divide attention between two fronts would further delay substantive American involvement with the war effort in Europe.