Do planets stop producing if you don't log in for a while? I figured I'd have 21.6k x30days worth of resources at least LOL

They do stop producing.

Three things stop production-
1. Inactivity (2 weeks)
2. Maxing out an item
3. Failure to have supporting material for the factories if any. In the case of troops failure to balance production.

__________________________
"Is not easily provoked"
Translated:
It is not good to wake a sleeping bear

this is half correct, if you do not log in prodution will stop only if there is no action performed on the planet.

You can be inactive for 2 years but if someone has been spying you planet, it will continue to update.

There are exceptions.