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Not really. You can use widgets and redraw when the user changes something, but this gets clumsy quickly.

Bokeh allows for interactive visualization though. Vispy[1] does to, by using webgl (but this require a running ipython kernel - so the plot will be static when exported to HTML).

This[2] is an interesting blog post about the future of python plotting/visualization.

[1] http://vispy.org/

[2] http://www.almarklein.org/future_vis.html

With matplotlib you don't need to redraw the whole plot or even the whole axes you can just change the data and update the relevant artist.

Yes, you can use the nbagg backend [1].

[1] http://matplotlib.org/users/whats_new.html#the-nbagg-backend

You can easily place the matplotlib plot in a widget and e.g. one can allow the user to control it with sliders and input boxes etc.