Memoir 44 Rules p. 14 wrote:
Movement: To move onto a Hedgerow hex, a unit must be adjacent to the Hedgerow. A unit that enters a Hedgerow must stop and may move no further on that turn. A unit that leaves a Hedgerow hex may only move onto an adjacent hex.
Battle: A unit may not battle the turn it moves onto a Hedgerow hex.
A unit may not battle the turn it enters a hedgerow, but there's nothing that says it can't battle when it exits. (Assuming, of course, that it's a type of unit that can battle when it moves 1 hex. Artillery wouldn't be able to battle when it exits a hedgerow because it can't battle when it moves. Almost all other units can.)