Of course, what you say is true, not that the vote mattered.
It just seems that the winning issue is to beat up Democrats with the War Mongering charge while they are the ones responsible and doing it.
The dirty little secret is that the Democrats wanted that war with Saddam just as bad as Bush did, they just put on that Kabuki Theater act for their base.
There are plenty of quotes from Democrats talking about fighting Saddam, before Bush was elected. Gore would have done the same exact thing had he won in 2000.