May you have consultant managing full time employees

You should have this discussion with a labor attorney. I know of companies that bring in short-term consultants to fill in for vacancies, such as maternity leave, etc.
The issue that would be of concern is whether this outside consultant continues to meet the definition of an Independent Contractor or if they are actually an employee.

There has been some new wrinkles (court decisions) relating to IC. You need to take a close look at the IRS and recent court decisions and see if they are truly meeting those rules.

For roles that can be done through professional services (i.e., controller, CFO) there is, in my opinion a little more wriggle room, not a free pass.

Yes. There is a thriving "rent-a-CFO" industry out there with everyone from independent consultants to Robert Half providing consulting finance leadership services. This runs from finance managers to controllers, treasurers and CFOs. And the companies utilizing those services run from private to large public companies. Those folks are, most assuredly, people managers. There is no reason you can't hire a consultant as a manager of FT employees.

The others have provided good feedback and direction. In my 20 years of experience as an outsourced CFO, our team has managed full time employees for many clients. One does not have to be an employee in order to be an officer or manager in a business. The board of directors can name a consultant as on officer of the business and can assure that she/he is covered by the company's director's & officers insurance. If you decide to follow this path, make sure that you have a good consulting agreement in place (i.e., get good legal support) and that the relationship is compliant with IRS and state guidelines on classification as an independent contractor. Also, you need to have the right to terminate the consulting engagement when it is best for your company to hire a full time person for the position.

Good Luck!