Yes, but there's no requirement they do so. They might (depending on the project) accept such a patch, but catering to forks of their project is rarely any OSS maintainer's top priority. Major distro forks can be important, but if someone built their own update checking mechanism they probably don't care too much about other installation methods.

Well, adding the option would significantly decrease the set of patches that the distributions need to apply, which would decrease erroneous bug reports, etc.

A distribution-provided package doesn't really need to be a fork unless upstream isn't playing nicely with the rest of the OSS ecosystem.