Generally hardware doesn’t call home, however drivers might do. You’re pretty safe using open source drivers on Linux I think. However, on Intel systems there still is the Intel Management Engine (IME) that’s kinda problematic. We know it got universal access and can be accessed via network even when the device is off, so it’s expected to include the backdoor Snowden talked us about (in case you know the movie: The one used to access the webcam without starting the Mac). Technically, there could be anything in there, we just don’t know. Same goes for AMDs Platform Security Processor (PSP), however that one doesn’t have access to the NIC and shouldn’t be accessible when the device is powered down.
Unfortunately, we also don’t know enough about all of this and there’s nothing we can do about it either, any speculation about it quickly becomes a slippery slope towards conspiracy theories.
There’s a tutorial on how to disable IME here in case you’re interested. User:Sakaki/Sakaki's EFI Install Guide/Disabling the Intel Management Engine - Gentoo Wiki