Lots of times. Check out the lead off hitter in this game from a current 2015 replay-type league:
www.whatifsports.com/slb/Boxscore.aspx
Even odder, I've seen batters pitch. Or at least noticed it many seasons after the fact, in a prog of mine. Mickey Cochrane got in a handful of appearances on the mound one season for a very bad (and presumably very fatigued) team. I posted about it somewhere in the
Believe It or Don't! thread -- Cochrane didn't pitch well, but I think had a slightly better ERA than his team overall.