Patching? Actually it should b Vulnerability Management cycle
Auto patching system may fail. I've seen that. In particular funny (sorry) was that I explained IT director that vulnerability scanning is standard way to check if patching works. He was not idiot but ... So, when they hired IT boss on the top of him and we resumed scanning, we found that 30% of computers were not patched while system reported they were. Then virus outbreak happened on the top of multiple vulnerabilities.
So, patching we discuss here IS NOT THE GOAL. It should be always Vulnerability Scanning after.
Is it possible to do within a month? Very hard. Almost impossible considering complex IT systems. The only one success story was when I did VM for Navy installation of 4,000 computers ten years back. Somehow IT guys managed to patch and I was able to do my scanning. Since that I see only sad stories.
The chaos result of of what we have now was created by IT giants rushing for profit no matter what.
They created the environment of "IT jungle" where we - the food for predators and them aka "hackers" - will coexist forever. The only one way to limit your risks is to limit your Internet connections. Pack your bag, forget your computer and go South. Bingo.