No, you can look at http://meritbadge.org/wiki/index.php/Special:Version
and see what extensions are installed. That information may be available by parsing server logs, but the information probably wouldn't be made available members of the public. The BSA does release information on how many merit badges of each type are earned, though. In 2013 about 6,500 boys earned cycling, which put it at #78 on the list, pretty much in the middle as far as the list of merit badges. I was a little surprised to see that horsemanship was earned by almost 11,000 boys. Anyway, the 2013 list: http://blog.scoutingmagazine.org/2014/0 ... -all-time/
The 2014 list probably won't be out for several more months.