Henry officially registered with the Gunners last week in time to face Leeds at the Emirates.
"Thierry is one of the Premier League's all-time greats, there is no doubt about that. And he will be desperately keen to make a fresh impact," Bromby said.
"I don't think it's a gamble bringing him back, he remains a class act. And, if you give him even the sniff of a chance in front of goal, he will punish you.
"If we can cut off the supply line to their strikers, then who knows? That's what we must do. There are always shocks in the Cup."
Leeds are currently eighth in the Championship with 38 points from 25 games.