Is it possible to add a column to a datatable read from a file?

I have a DataTable read from a csv file:

ID,ItemCode,ItemDescription
1,Test0,test item
2,Test2,second test item

When I try to create an additional column as in https://learn.microsoft.com/en-us/dotnet/framework/data/adonet/dataset-datatable-dataview/adding-columns-to-a-datatable, it silently fails. The code:

dataTable.TableName = "test"
dataTable.Columns.Add("MyTestColumn", GetType(String))
dataTable.AcceptChanges()
Using sw As StringWriter = New StringWriter()
    dataTable.WriteXml(sw)
    Console.WriteLine(sw)
End Using

has output

<DocumentElement>
  <test>
    <Column1>ID</Column1>
    <Column2>ItemCode</Column2>
    <Column3>ItemDescription</Column3>
  </test>
  <test>
    <Column1>1</Column1>
    <Column2>Test0</Column2>
    <Column3>test item</Column3>
  </test>
  <test>
    <Column1>2</Column1>
    <Column2>Test2</Column2>
    <Column3>second test item</Column3>
  </test>
</DocumentElement>

Is it possible to add a column in this way?