Does Action<T> prevent enclosing class instance to be GCed when all other references to class instance are removed?

I wonder whether Action<T> prevents an enclosing class instance to be garbage collected when all other references to such class instance are removed during runtime?

public class Class1
{
    private Action<string> _callback;

    public Class1(Action<string> callback)
    {
        _callback = callback;
    }

    public void DoSomething(string msg)
    {
        _callback(msg);
    }

}

public class Class2
{
    private List<Class1> _class1s;

    public Class2()
    {
        _class1s = new List<Class1>();
    }

    public void AddClass1Instance()
    {
        _class1s.Add(new Class1(OnClass1DoSomething));
    }

    public void RemoveLastClass1Instance()
    {
        if(_class1s.Count > 0)
        {
            _class1s.RemoveAt(_class1s.Count - 1);
        }
    }

    private void OnClass1DoSomething(string msg)
    {

    }

}

In this simplistic example, when I call RemoveLastClass1Instance() within Class2 will the Class1 instance be garbage collected or does it remain to hold reference to OnClass1DoSomething() via Action<string>? My goal is to completely remove Class1 instances and have them garbage collected.

EDIT: (further to Jon Skeet's comments, I added the following code to better understand

public class Class1
{
    public event Action<string> Event;

    public Class1()
    {

    }

    public void DoSomething(string msg)
    {
        var handle = Event;
        if (handle != null)
        {
            handle(msg);
        }
    }

}

public class Class2
{
    private List<Class1> _class1s;

    public Class2()
    {
        _class1s = new List<Class1>();
    }

    public void AddClass1Instance()
    {
        var newClass1Instance = new Class1();
        newClass1Instance.Event += OnClass1DoSomething;
        _class1s.Add(newClass1Instance);
    }

    public void RemoveLastClass1Instance()
    {
        if(_class1s.Count > 0)
        {
            _class1s.RemoveAt(_class1s.Count - 1);
        }
    }

    private void OnClass1DoSomething(string msg)
    {

    }

}