It can if it has hit the deck at some point during the turn, after the first time it has entered battle.
it has to hit deck?
Change to Banding generic Characters
The restriction upon entering battle multiple times per turn is only limited to unique characters. Generic characters can enter battle more than once per turn.
from http://www.cactusgamedesign.com/message_boards/redemption-official-rules/rule-changesclarifications-for-2011-2012-tournament-season/msg434385/#new
that doesn't mention that limitation