Do you know if you can update a switch that has an installed homebrew. So quite normal via the software update or does the homebrew no longer work?
Updating a switch with an installed homebrew immediately means tuning his car illegally and then driving up to the TÜV.
Installing cell phones to jailbreak or homebrew indirectly means that you actually say goodbye to the software updates from the manufacturers, with the exception, of course, that a newer homebrew version is already available for a newer system version.
So, my answer is: Yes, the homebrew status would be lost because I assume that the system will follow up missing security updates and block its access.