Suppose that I have the following code:

private void UpdateDB(QuoteDataSet dataSet, Strint tableName)
{
    using(SQLiteConnection conn = new SQLiteConnection(_connectionString))
    {
        conn.Open();
        using (SQLiteTransaction transaction = conn.BeginTransaction())
        {
            using (SQLiteCommand cmd = new SQLiteCommand("SELECT * FROM " + tableName, conn))
            {
                using (SQLiteDataAdapter sqliteAdapter = new SQLiteDataAdapter())
                {
                    sqliteAdapter.Update(dataSet, tableName);
                }
            }
            transaction.Commit();
        }
    }
}

The C# documentation states that with a using statement the object within the scope will be disposed and I've seen several places where it's suggested that we don't need to use try/finally clause.

I usually surround my connections with a try/finally, and I always close the connection in the finally clause. Given the above code, is it reasonable to assume that the connection will be closed if there is an exception?