Well I'm talking purely from a usability perspective; where I have to disagree. I agree that no one size necessarily fits all and that navigation (particularly navigation systems that stay in focus regardless of scrolling) get in the way on mobiles.
From our end user testing we've found that; particularly with more casual computer users and older users; tend to get taken by surprise by collapsing navigation systems that hide away; even into an icon that may be obvious to you or I; importantly as savvy users who are used to this kind of UI both online and in software applications. Of course whether this is really a problem depends on a sites audience.
Even then, the basic fundamentals of UI design teach not to have Pandora's Box style navigation systems, of which this kind of UI is a textbook example (collapsing a navigation away into a button).
Therefore, unless absolutely necessary I would try to avoid doing this and would instead investigate alternative approaches, even if that means having to be a bit more inventive or even handle the UI slightly differently on a mobile. Having a responsive design doesn't mean you can't have platform specific deviation where it is better for the end-user to do so.
But that's based on an assumptions that may not be true.
For one, a user may not intentionally collapse the menu; on touch devices its not difficult to do. If the menu slides away then they may well just hit the button again, however end users don't always react like this; in fact they tend to react in every way you expect them not to react; and the less savvy they are the more this becomes true.