The blog already has a Sitemap but does it requires a Random Post button/plug-in?
Or is the drip feed 2-3 post a day and 'Other posts of interest' enough?
In the post 'Increased traffic by 50%' Jacob says that the plug-in that lists 'Other posts of interest' increased site traffic/pageviews.
So having a Random Post button might help unique/new visitors to stick-around longer and come back.