mabuhay if it was operating at FL3++ and clearly looked like a widebody jet, they would have NO instantaneous interest in it.
Military outfits are almost entirely monday-friday 9-5 operations, it would take a stuka attack from something very fast moving, heading directly for a military base or major population centre to sound any alarm bells in the mind of the poor guy on duty at O-silly-hundred-hours observing for credible threats.