It seems exceptionally heavy handed but going by the rule anything publicly available should be tested should auto-implemented properties be tested?

Customer Class

public class Customer
{
    public string EmailAddr { get; set; }
}

Tested by

[TestClass]
public class CustomerTests : TestClassBase
{
    [TestMethod]
    public void CanSetCustomerEmailAddress()
    {
        //Arrange
        Customer customer = new Customer();

        //Act
        customer.EmailAddr = "[email protected]";

        //Assert
        Assert.AreEqual("[email protected]", customer.EmailAddr);
    }
}