Not anymore. Housing allowances are paid directly to the lodging provider, it’s no longer included in per diem.
Because people used to stack up in Kim’s for the cheaper rate to pocket the difference, you can’t do that anymore. Apparently a government shutdown led to people not getting per diem paid out so then they had to pay out of pocket for their housing until congress pulled it together and passed a budget. Now it’s all done out of a central account to the housing provider directly. So people don’t get screwed by the wheels of government.