No - it won't happen. The core editor is open source.
At best, MS has some limitations around running some plugins (that they also develop) that require the licensed version of VSCode, rather than the OSS build.
Most of those plugins either use MS servers (ex: Live Share) or use toolchains that MS is historically more closed with (their C++ toolchains).
Generally speaking - you can use OSS Code today, without any issues. There's a flatpak here https://flathub.org/apps/details/com.visualstudio.code-oss and many distros package it as the default...
I run arch and it's in the repos as simply "code" - https://archlinux.org/packages/?name=code
I run this as my default everywhere, and it works a-ok. There is a small subset of devs that would likely feel some pain losing the closed extensions, but the total impact feels overblown to me.