Likely, no as the package manager would give it back the setuid bit.
Create a list of all current setuid and setgid binaries before running this and then you can just give the setuid/setgid bit back to them.
A list of all setuid and setgid binaries can be gotten by running
find / -type f \( -perm -4000 -o -perm -2000 \)
Assuming you haven’t given the binary the required capabilities, it will not work. Some binaries like su will pretend to work but then always give a permission denied error.
We can create a list of common setuid and setgid binaries that are usually found on a system and remove their setuid/setgid bits individually. This way, we have a lot more control over what happens but there may be certain binaries that slip past.
Not that I know of.
The Arch Wiki has a page on this that may be useful.