That's not what using AOSP would mean, as it's just the operating system codebase. You can create an operating system from Android source code, deploy, and use it without ever contacting Google.
That being said, I doubt the Switch's OS is based on AOSP, as there's not really any code there that would be useful for a gaming OS over more basic UNIX codebases.
AOSP is a fully open source codebase, and Google would have nothing to do with it. So what you write there wouldn't be happening at all.
You can perfectly use AOSP's kernel just as flexible as you could use vanilla unix or bsd afaik.
Google is the "leader" of that project, so I do NOT trust it then. Period. IF they don't have anything in there that datamines, it still helps their Datamining shit by making their OS more popular and thus on more phones, consoles and other machines. I do not like that, nor do I want that. I do not want 1 overlord to rule all the datamining companies.
If you are going ot use a Linux Kernel or BSD? Go for Debian, RedHat or OpenBSD and FreeBSD. Why should I use a Google inspired Linux kernel which I can't trust or only helps to make them the biggest player? I know what AOSP is, I simply want nothing to do with it.