I doubt it. As I understand it, it's a basic convention in diplomacy that embassies and their people don't pay taxes. Period. Even if part of the embassy is used
to house someone rather than for office space, does not make a difference.
For many years, London has been trying to negotiate for US diplomats to pay London's congestion charge. No way. The embassy sees it as a tax and refuses - not just for cars on official business.