Yes that's right next to the message button that is already present on mobile, is it possible to set it up by changing code for example?
Add user avatar onto see all notifications
There's probably a few other things that could be done on this page, but adding the users avatar of whom up voted, mentioned etc would be a nice addition, perhaps even lay it out in by similar way to topics, rather than the current grey on lighter grey that's currently there.
It's good for seeing all past notifications, but it could be extended in the future to include "notable topics" maybe stickies or "promoted topics", things like that. I'm not sure how many the drop down shows at any one time, so if you're mr popular, you might miss a few because it only shows the last 10 for example.