As Grover posts, you DO NEED the admin user.

You DO NOT NEED the admin employee.

It would be better to inactivate the employee rather than delete, in case there are any modules that rely on that record. This way no employee related document can be created, but no problems will occur if a module looks for the admin employee record.

On every system there is someone who has more rights than the others, but that doesn't mean that some employee is going to be paid only for being the administrator, you can be the administrator but also you can have another role on the system. When something happens then you can enter and solve it. Why you can't delete this user? Because Admin user has ALL the power and even when you have more admins anyone is going to have the same rights. By default the system has SUPERUSER=1, so the admin needs to be there ALWAYS.