If I'm not mistaken a officer can be called up at anytime.
At least that is how it use to be back in the 60's
You're partially mistaken. A reserve officer in the Standby reserve cannot be involuntarily called up except by act of Congress. The President can on his own hook activate the ready reserve. The Ready Reserve includes the Selected Reserve (AKA participating or drilling reservists) the standard reserve units plus individual mobilization augmentees. The RR also includes the IRR, which is made up of people with time left on their Military Service Obligation (generally 6 years) and certain retirees.
This guy, if he had completed his resignation, would not fall into any of the categories of reservist, he'd be a PFC (Private F'n Civilian).
That said, resigning in the middle of a war is not something I would do, I don't believe. In fact if the want me today, they can have me. As it is I'm working on a Army post as a technical adviser contractor.