Not really, no. Messier had great respect for all his opponents.
A half-dozen times or so in a 26-year career he crossed the line into dangerous plays, but in all cases I've seen he simply lost his temper in the heat of the battle. He was an intense player with a physical edge. I never once saw Messier wack a guy with his stick.
Also, Messier didn't go after elite players like Mario or Yzerman, ala Gary Suter. (Yeah, I know he elbowed Mike Modano in a collision, but that's more an example of him raising an elbow to protect himself in anticipation of a hit. He didn't know who the player was. Also, we got that stretcher-fail clip from that incident, which makes it worth it.)
Sometimes he hit smaller guys, but Messier also answered the bell by fighting with McSorley (3 times, I think), Peplinski, Roberts, many others, etc.
If you're going to call Messier the dirtiest guy ever, you have to do the same for Gary Roberts, Eric Lindros, Gordie Howe, etc. It was a different time with different standards.