I'm using Sublime Text 2 and 3, and the same issue occurs in both. Control+backtick (defined as "Show Console") does not register. From checking sublime.log_commands, it looks like this key is not being recognised at all. However, Control+single quote does work for "Show Console" - even though it is not defined as a key binding at all in the defaults.
This is with a UK keyboard (where backtick is on the top left key, just above tab, and single quote is on the key to the right of semicolon). I've tried a keyboard macro program, and it reports that backtick on my keyboard is virtual key 223.
Yes, UK here too and ctrl+apostrophe (right of semicolon) does the trick here under windows, but backtick does not work.
On my linux laptops however it's the backtick key. The confusion between the two OSes is quite annoying, but not nearly so annoying as not being able to rid myself of the menubar in distraction free mode under linux