We've talked a lot about this internally and have decided to not do implement this at the moment.
The reasoning comes out from two points:
The navigation bar should not be context specific to the current view. It's confusing when the contents of a sliding panel change based on what you're presently looking at, and doing this would be a drastic change for the navigation bar.
This is a power-user only feature, and although we implement a lot of power-user centric features this one doesn't make much sense because if you're someone who already knows what a meta site is you most likely know that there's an "EDIT" button next the "Your Sites" field too.
At the end of the day, I can't really think of this being a positive gain since it'll confuse new people a lot (it'll take some practice to realize sliding the navigation drawer from different places does different things) and the field right below it is customizable to remedy this situation.
One minor note: We have discussed completely redoing the navigation of the application to turn taps on an item in "YOUR SITES" from displaying the site to popping something open below the item that lets you have easy access to questions, tags, users, favorite tags, etc. If we do end up doing this (which I think we will) then adding a meta link here will be an obvious move.