There are two potential problems here.
Firstly, you need to make your shell expand aliases after `sudo`:
alias sudo='sudo '
From `man bash`:
> If the last character of the alias value is a blank, then the next command word following the alias is also checked for alias expansion.
Secondly, on many distributions, `$PATH` is not propagated to the new shell by sudo. You can manually change `secure_path` to add the directory which the `sublime_text` executable is in:
Defaults secure_path = [...]:/usr/local/share/applications/sublime-text-3
...or you can disable secure_path altogether (note: `secure_path` makes sure that an attacker cannot change your path and use it to influence the command you will run as root, so consider this carefully):
Defaults !secure_path