These would be interesting and fun stats to see, but I have to wonder whether adding this really have the desired effect. Would users feel that they need to close vote more? Or would it contribute to the "that's a big pile of close votes; I won't even make a dent so screw it" effect?
Additionally, since we're capped on the number of votes per day and can only vote once per question, there's an important choice to make on how to spend them. Do we vote against questions already in the queue, or jump on crappy new questions just posted? If the queue is growing in size, it seems the latter happens more often, on average.
The speed of casting votes doesn't really matter; it's the allocation which governs the change in queue size. We could implement a quota requiring X percent of votes per day be cast against questions already in the queue, but I suspect this would be quite unpopular. There are probably much better ideas out there for motivating this behavior; I'm just throwing that out as an example.
Rather than encourage users to focus on items in the close queue, or in tandem with doing so, we could encourage them to spend all their votes every day. The size of the queue strongly suggests that not all users do this. The obvious method to encourage doing so would be adding a new badge set.
Overall, I like this idea, and encouraging users to tackle the close vote queue is definitely worth doing. I'm simply not sure whether passive methods such as showing stats would be effective enough (read: worth spending dev time on when there are potentially better methods to achieve the same goals). A little bit of positive reinforcement goes a long way.
The opposite would be to motivate new users to not create more bad questions.
I think this goal is both more worthy and far more difficult.