Linking a User account to an employee record by programming (API or C#)

Yes.  In C#, just set Employee.UserID = to the Users.PKID, just as you stated.

In the following code, request an object for a custom DAC containing the AcctCD value on the EPEmployee record for which I want to link the User account.  Username contains the existing user (by login name) that I want to link to the employee.  This is significantly reduced to relevant code for your question, but I actually took this from a set of code where I create a user, the employee, the contact records for the employee, and link it all together.  However, this little bit should make the link you requested if your User and Employee exist.  Just replace the “request” references to your own variables/values.

EmployeeMaint graph = PXGraph.CreateInstance<EmployeeMaint>();
EPEmployee employee = graph.Employee.Search<EPEmployee.acctCD>(request.EPAcctCD);

AccessUsers graphUser = PXGraph.CreateInstance<AccessUsers>();
Users user = graphUser.UserList.Search<Users.username>(request.Username);

employee.UserID = user?.PKID;
graph.CurrentEmployee.Update(employee);

graph.Save.Press();