I am running Ubuntu 16.04.4 and have installed Sublime from your repository, I couldn’t see Sublime as a selection in the ‘Open with’ program list.
I tried the answer here https://askubuntu.com/questions/396938/how-do-i-make-sublime-text-3-the-default-text-editor but the only way I can get this to work is if I rename sublime_text.desktop to sublime-text.desktop within /usr/share/applications.
Question is if I update Sublime will I lose this setting? Is it even a Sublime setting Has this been reported?