As you asked a question Don, I will offer an answer. I would say it's not possible it needs to be enabled. If the NTP is configured, by default the 4K will use it, unless there's been the exec-date and NOSYNC change as George mentions above. At least, that's true for the RMX. The platform OS would use it. The only issue I ever have with NTP is the dispersion parameter needs a tweak or the OS will ignore the NTP reply from the server.. edited either by tos field in ntp.conf or if the server is a Windows box you can change it in the windows registry. If wireshark shows you have received an NTP reply but the 4K is ignoring it, for me tos/dispersion edit has always resolved.
Hard to say what's going on, from the original post. I would push a good time and date into the OS and the hwclock like I mentioned, and then try some restarts/reloads, see what it did. I wouldn't expect it to be battery if the processors weren't powered down, but as Sherlock Holmes said...If you have eliminated the impossible, then what remains....