Is it possible for a branch office in Shanghai to pay social security for its employees, but the payroll is paid by the head office? Is there a problem with payroll reporting and auditing?

Personally, I don't think there's any impact, the two parts are completely divisible, the financial accounting is also separate. If the branch is a separate set of accounts accounting, with the current account instead of the relevant expense account can be.

What you mean by "declare wages" is to declare to the head office? If so, then these two parts can be declared separately, or only the amount of salary to be paid to employees (according to the management requirements of the head office to declare).

This is not a problem for auditing, which is a normal part of internal management, and the auditor will only be concerned about whether the accounting treatment is in line with the requirements.