Not sure that update checking even makes sense if Audacity is provided by the distro. It should be taken care of by the normal check for updated packages in the distro’s repo (and won’t need to go anywhere near the Audacity project’s web server) - unless you manually install a later version of Audacity bypassing the distro’s repo, for example.
I think the decision to use a fork is a finely balanced one - since every fork fragments the user base and spreads the developer resources more thinly.