It depends - basically on bikes nowadays the critical dimension is saddle-handlebar drop as it's harder to change than others. He will probably be fittable to a 54, though if he has racing ambitions I would suggest that it could be a bit short. For example I am 5'9" and ride a 55 Pinarello with a 12cm stem and Deda bars with a long reach. Yes you can get 14cm stems, but I think 10-12cm is the sweet spot.

On the other hand the 56 head tube could be too high if he likes a short, low position, but this is less likely IMO.

Best alternative I think is to get him to go to his LBS for a test ride on a 56 or a professional fit. To assuage his guilty conscience he should at least buy some shorts, tubes and a puncture kit from them.