Yes, he can do that; however when he files his personal income tax, he will be limited to the lesser of 3 amounts:
1)The amount actually spent on eligible housing expenses FOR ONE HOME
2)The fair market rental value plus furnishings and utilities
3)The amount officially designated in advance and paid by the organization as a housing allowance
...to claim as his housing exclusion tax benefit, so if he is paid more in housing allowance payments than he has eligible receipts for...the rest will be reported as income.