There should be no problem using a client code (unless prohibited by hotel contract). Unfortunately, not many are privy to the contract terms and not everyone at the company is "authorized" to extend usage to a non-employee. There is a local CY that has a sign posted at the front desk that specifically states our company contractors are NOT allowed to use the company rate (and yes, our company was called out specifically!). Personally made us sound cheap.

Often, when bringing in candidates for interviews, we've had to provide a property with a letter stating names and dates of arrival. And if we were paying for any part of the stay, specify what we were covering (typically room & tax only). Along with the department code to be billed.