>Yes, because the military can't follow an illegal order, which is what a declaration of war without the approval of Congress would be.

Congress hasn't actually declared a war since World War 2. The President sends troops wherever he likes, whenever he likes, for whatever purpose he likes and Congress rubber-stamps their approval after the fact, and they call it something other than a war.

You're correct that the military can't follow illegal orders, but what you're describing as an example of an illegal order is just the way the US military industrial complex works.

In every major conflict since the creation of the war powers act became law, an authorization for the use of military force was passed by Congress prior to major combat operations. This was true in the Gulf War, the War in Afghanistan, and the War in Iraq. There were cases where the president invoked the war powers act for short term deployments of forces, which did later result in Congress authorizing additional use of force (e.g. Lebanon), but nothing even close to the scale of invading a stable, sovereign state.