Esto parecería implicar "no". Lo cual es lamentable.

[AttributeUsage(AttributeTargets.Interface | AttributeTargets.Class,
 AllowMultiple = true, Inherited = true)]
public class CustomDescriptionAttribute : Attribute
{
    public string Description { get; private set; }

    public CustomDescriptionAttribute(string description)
    {
        Description = description;
    }
}

[CustomDescription("IProjectController")]
public interface IProjectController
{
    void Create(string projectName);
}

internal class ProjectController : IProjectController
{
    public void Create(string projectName)
    {
    }
}

[TestFixture]
public class CustomDescriptionAttributeTests
{
    [Test]
    public void ProjectController_ShouldHaveCustomDescriptionAttribute()
    {
        Type type = typeof(ProjectController);
        object[] attributes = type.GetCustomAttributes(
            typeof(CustomDescriptionAttribute),
            true);

        // NUnit.Framework.AssertionException:   Expected: 1   But was:  0
        Assert.AreEqual(1, attributes.Length);
    }
}

¿Puede una clase heredar atributos de una interfaz? ¿O estoy ladrando el árbol equivocado aquí?