Can A Government Employee not be a Government Employee?

This morning, while I was in the shower, an odd question popped into my head:

• If President Trump or a Cabinet Head elects to take no salary, are they a government employee?

Here’s why that question occurred to me: Ethics rules, disclosure rules, conflict of interest rules, rules about accepting gifts, and all other sorts of regulations apply to government employees. But Trump is nominating millionaires and billionaires who don’t need the salary. Many of them have publicly said they will not take a salary. So does this make them exempt from all the regulations that apply to government employees? Further, note that it means they will not have taxes taken from their salaries (avoiding taxes), and their income will be primarily capital gains on investments (which is a much lower tax rate, and can be offset by losses reducing taxes even further). No salary, and income primarily from capital gains also puts them in a lower tax bracket (I think — I could be wrong there).

So, by refusing a salary, could they both avoid those pesky regulations and lower their taxes? Could this be why we are seeing so many millionaires and billionaires being nominated?

[ETA: Conclusion: (•) Salaries are defined by statute, and must be paid — then they can be subsequently donated, returned to the Treasury, etc.; (•) Volunteering for government service is not allow, so they have to accept a token of $1; (•) even if they did volunteer, there are volunteer agreements to cover ethics.]