I regularly "deep freeze" or make read-only systems from Raspberry Pi, Ubuntu, Linux Mint LMDE and others Linux Distros whereas I disable automatic updates everywhere (except for some obvious config/network/hardware/subsystem changes I control separately).

I have had systems running 24/7 (no internet, WiFi) for 2-3 years before I got around to update/upgrade them. Almost never had an issue. I always expected some serious issues but the Linux package management and upgrade system is surprisingly robust. Obviously, I don't install new software on a old system before updating/upgrading (learned that early on empirically).

Automatic updates are generally beneficial and helps avoid future compatibility/dependency issues on active systems with frequent user interaction.

However, on embedded/single purpose/long distance/dedicated or ephemeral application, (unsupervised) automatic updates may break how the custom/main software may interact with the platform. Causing irreversible issues with the purpose it was built for or negatively impact other parts of closed circuit systems (for example: longitudinal environmental monitoring, fauna and flora observation studies, climate monitoring stations, etc.)

Generally, any kind of update imply some level of supervision and testing, otherwise things could break silently without anyone noticing. Until a critical situation arises and everything break loose and it is too late/too demanding/too costly to try to fix or recover within a impossibly short window of time.