No he's not even right about that. Congress authorized war powers; there is no Constitutional requirement that the empowering document contain the phrase "declaration of war". And even aside from that - even if you could make a case that, for example, it's not a 'real' or 'legitimate' war because it "wasn't declared" - it still wouldn't make Bush's use of force "illegal". Congress authorized force and Bush ordered it; how is any of that "illegal" (=prohibited by some law)? which law is the war against exactly?
At the Texas Straw Poll, Paul called what we did an illegal act of aggression. He called us the aggressors. In fact, we were enforcing a contract that was the consequence of Saddam’s aggression in the First Gulf War. He had continued to test and push against any restrictions.
Congress voted to authorize the President to use all force necessary. That’s all that was necessary.