Typically they do, the infrastructure is there with automatic updates and C&C-like abilities. The driver runs close to the kernel to be able to use hooks into files closing and so on, at least on MICROS~1 operating systems.
Did the Crowdstrike thing earlier this year reach you? They sell a corporate version of this kind of trojan, and did a fuckup in an update, suddenly making a lot of people realise that someone else has control over their computers.
Sophos was the latest scandal. Though, it's unclear to me to which degree their antivirus tools helped to install the malware. Maybe it was just the target selection from telemetry data. Maybe they used it to deploy the "kernel implant"?
Disclosure, worked there 15 years ago.