bcc: chromium-dev
+cc: net-dev
"It depends" - but to do so reliably directly would require either poking more holes in the sandbox or proactively notifying the (potentially hostile) renderer, both of which can serve as information leaks.
The former should not be possible today, and the latter is only practiced in a few limited cases, specific to the feature, and not in a generalized way. For example, the socket APIs dispatch an event of network interfaces changing, rather than when the user changes network, such as for WebRTC, and only when the renderer is using WebRTC. And this is before getting into things like S13N and whether the browser will even be monitoring for these events going forward.
Since it sounds like you're going to be crossing a privilege/security boundary, could you explain a bit more about what code you're moving?