Meat damage from a broadhead is negligible, but the open wound does allow for some dirt and debris to contact the meat.

However, hopefully your shot will be through rib meat only which most don't eat anyhow, so there SHOULD be no meat loss at all!

There are some precautions to take if you are shooting carbons however, especially if your arrow breaks.

Check out this link for carbon arrow issues when bowhunting:
http://www.beman.com/safety/