If not, what were his other reasons for getting the U.S. involved in WWI?
^ these previous answers I've given should be pertinent
In a sense yes, he did involve the United States in the war for reasons like that, but it had much less to do with him personally having a seat as it did the United States in general being represented. The United States had offered before to mediate/arbitrate negotiations to end the war, and these had been rebuffed; with the more extreme turn the war was taking in 1917, it was clear that not only could the United States not remain aloof of the struggle going on around it, but that involvement would be necessary to ensure a settlement that would bring a degree of relative peace and security to the United States.
By 1917, the Allied Powers (Britain, France, Russia, Italy) were in a position in which they could foresee a victory over the Central Powers, but were themselves fairly exhausted. It's unlikely, for example, that the exertions of the British Army in Flanders in 1917 could have been sustained without direct government-to-government loans from the US. April would see the failure of the Nivelle Offensive, and the paralysis of a significant part of the French Army by mutinies, which I discuss here. Russia would experience Revolution in March (February), leading to the establishment of a republic. 1917 would also see the Allied governments in general begin to make firm statements on war aims (something that did not occur to the same degree among the Central Powers), emphasising more often than not minimal territorial gains, with things like disarmament, an end to German aggression, etc. at the forefront. The political landscape was changing, to where the United States could feel confident in supporting the allies, while pursuing more democratic aims themselves. Wilson's statement about making the world safe for democracy makes a little more sense here.
At the same time, there were very practical, national security reasons for the United States to enter the fight. American civilians had lost their lives since 1915 at the hands of German U-boats, Lusitania and Sussex just to name a few. The latter sinking led to a pledge by the German government in 1916 that they would not pursue USW in the future. Under Hindenburg and Ludendorff's 3rd OHL (supreme war command), that along with many other 'rules in the book' so to speak were thrown out. Unrestricted Submarine Warfare was again unleashed, the Alberich Bewegung in northern France saw wanton destruction of property, French and Belgian civilians were being deported to the Reich as forced labour, reprisals against Allied prisoners of war escalated, and attacks on civilian targets with Zeppelins and Goth bombers ensued. It was clear that those in charge in Germany could not be expected to produce a settlement in which things like sovereignty and international law and customs meant anything more than words on paper.
Add to this that the German embassy had been financing and carrying out domestic terrorism, sabotage, and espionage on American soil since 1915, the Vanceboro Bridge bombing an excellent example, and the Zimmerman Telegram, which invited Japan and Mexico to attack America to divert attention from Germany, there was no way the United States was going to avoid the war indefinitely. Moreover, American lives, interests, and security were at stake now.
So yes, American involvement in a postwar settlement was an important priority, but it wasn't the only one, and moreover, is was certainly well founded based on what was taking place in Europe.