For what it's worth, I've been running Windows 11 full-time on both Skylake ("sixth generation") and Ivy Bridge-EP ("third generation") systems without issue, though not for gaming.
Assuming your system meets all other Windows 11 system requirements (TPM 2.0, etc.), you should have no problem installing Windows 11. You'll have to download it yourself and trigger the upgrade manually (mount the ISO and run "setup.exe"), and click through a warning message, but AFAIK no other workarounds are required.
Whether doing so is advisable depends on your appetite for risk, but I'd personally be more worried about application developers than Microsoft when it comes to breaking changes in the future: Windows 11 updates have to remain compatible with every CPU on the supported list*; new applications and version upgrades have no similar requirements.
* AFAIK, this does not necessarily apply to new Windows 11 versions, though even here, I'd expect fewer breaking changes than with applications and games that typically have stricter CPU requirements to begin with.