The trick here is to cast the Connection property of the ObjectContext to the type System.Data.EntityClient.EntityConnection. Then you can access the StoreConnection property:

var dataTable = new DataTable
{
    Columns = { new DataColumn("Value", typeof(string)) }
};
dataTable.Rows.Add("first row");
dataTable.Rows.Add("second row");
dataTable.Rows.Add("third row");

//
// EF does not support table-valued parameters, so we'll do it ourselves
//
using (var ctx = new MyObjectContext())
using (var cn = new SqlConnection(((System.Data.EntityClient.EntityConnection)ctx.Connection).StoreConnection.ConnectionString))
using (var cmd = cn.CreateCommand())
{
    cmd.CommandText = "SomeRealyCoolStoredProcedure";
    cmd.CommandType = CommandType.StoredProcedure;

    cmd.Parameters.AddWithValue("ID", 123456);
    cmd.Parameters.AddWithValue("ValuesTable", dt).TypeName = "MyTableType";

    cn.Open();
    cmd.ExecuteNonQuery();
}