NTP is not a critical service, yes its used to sync time, but it is not a critical service required to communicate only accurate time.
Smart Bombs use GPS, GPS has its own time and is far more accurate than NTP.
Utility infrastructure is fucked already.
GPS can be spoofed and jammed, most smart munitions have backup mechanisms because of this. Public knowledge.
Bombs wouldnt fly off course. Most long range has multiple systems to account for GPS flaws and breakdowns. Typically other sensors. The internet is not used to initialize, configure and/or launch these systems.
Yes, if the internet went down, people would panic. Sad fact, but there is still raw radio waves that can and would be used in an emergency.