I went with my husband and 3 daughters to some of the NYC protests and never saw that, but I do not doubt it. The reason was likely his vote. Edwards, Lieberman and Gephardt were in favor of going to war - and supported that decision even months after the invasion and all three were co-sponsors of their houses bill. Kerry wasn't. Edwards was extremely pro-war even 6 months after the invasion.
In addition, many in the far left of the party, disliked Kerry from 1971. They resented the attention he got, even though he was by far the most powerful anti-war voice. They disliked that he argued for staying in the system and changing it, while they argued for revolution.
The fact is that the anti-war movement did go completely behind Dean, but voters in Iowa and elsewhere, who identified themselves as having been against the war, split for Kerry - not Dean. In Iowa and NH, the reason was that Kerry was there in late 2002 and he said things like "America does not go to war unless it has to" and he was still arguing against the war until Bush invaded. Person to person, people knew he was not pro-war.
Dean's and Kerry's comments on talk shows and interviews in September and October 2002 did not place them far apart - both wanted to avoid war. Kerry in summer 2002 was one of the leading voices arguing that it was wrong to go without going to the UN and Congress. Dean was not a pacifist either - constantly making the case that he would have voted for Gulf War 1, which even Senator Lugar said in a SFRC hearing this year was a war for oil. It was legitimate for Dean to use Kerry's vote - but, it is not 100% clear how he would have voted. He had said he would vote for Biden/Lugar, but that was the bill that Kerry preferred as well - and it was not the bill voted on. There is NO pre-vote comment on his part against the bill.
In case you don't know, the significance of saying it was "not the last resort" was a way of saying it was not a just war. This is from Catholic St Augustine theology - and if you doubt that is how Kerry meant it - listen or read his speech at Pepperdine.
http://www.pepperdine.edu/pr/releases/2006/september/kerry.htm (This is a 2006 speech on religion and faith and how they inform action. )
If you listened to Kennedy speak for Kerry in Iowa, he did not shy away from speaking of Iraq. In addition, you ignore that in 2005 and 2006, Kerry had a stronger position for exiting Iraq than Dean, who supported the Korb plan.