To us, the general Westerner, no. You say 'general office' to me, and this is the main office of a large department at a University, or a hospital, or school etc, where the receptionist and typists are located.
Most Westerners in China would probably be there on business and they would know the difference:
9. <Ministry of Justice of China>
The oversea Law Firms’ applications for establishing offices are required to be examined and approved by the Ministry of Justice of China.
In addition to the above-mentioned authorities, the other Chinese governmental authorities which are in charge of the industries other than the above would accept and approve the applications of the foreign companies engaged in other business fields. In the event that a foreign company engaged in several different industries simultaneously applies for a comprehensive office in China, the Ministry of Commerce, as the mainly designated authority, would accept the application and perform its examining & approval function together with other relevant authorities.
National Centre for AIDS/STD
The office of Director was established on July.1st,1998. At the beginning, it was a comprehensive office including financial affairs, human resource management and laboratory and logistics affairs. Later on these three functions were developed into separate representations.
(Each became a 'general office').