Hi @schmersgahoven,
You can look at my BBQ project here. Cayenne does not control any of the digital I/O directly as I use Virtuals for interacting with Cayenne. Also, all decision making is done by the PID and timers. The only thing Cayenne does is start and stop the action and provide a setpoint. Cayenne monitors and displays my temperatures and the state of operation.
I expect that if the internet connection died, that it would continue to function, Especially if you had an additional set of local controls.
Cheers,
Craig