Would it be correct use of the new modifier in this context?
Technically - yes, there will no errors or warnings.
As for me, using of new keyword itself as a modifier indicates a design drawback.
I'll give one example.
public class MyList<T> : List<T>
{
    public int AddCallsCount;
    public new void Add(T t)
    {
        AddCallsCount++;
        base.Add(t);
    }
}
[TestClass]
public class Test
{
    [TestMethod]
    public void TestThatsNotGood()
    {
        List<object> list = new MyList<object>();
        list.Add(1);
        list.Add(2);
        MyList<object> myList = list as MyList<object>;
        Assert.AreEqual(0, myList.AddCallsCount);
    }
}
It looks like polymorphism works, but actually does not.
UPDATE:
Ok, there is very simplified explanation. I omit explanation of what polymorphism is. 
Polymorphims is realized with implementation of abstract\virtual and overriding methods. As soon as neither virtual nor override modifiers are specified MyList<T>.Add is just another 'common' public method. And with MyList<T> inherited List<T>, MyList<T>.Add 'hides' List<T>.Add because name and parameters of both methods are same.
At lower level: as soon as List<T> type definition of method Add isn't marked with virtual keyword, compiler won't search for overriding methods of actual instance type (MyList<T> in this certain case) for variable of given type (List<T> in this certain case).
Definetely it may lead to logic errors and incorrect usage of class API.
Hence, compiler 'thinks' that probably there is a logical mistake or design drawback and warns programmer. The new keyword is just a way to talk to the compiler 
yes, I know that it's not good, but I need it because of my bad design
.