Merit of using a small sample of data for hyperparameter tuning

Question

In the section Blueprint recap and conclusion of this notebook, the author used only 20% of the data for the hyperparameter tuning with Grid Search as shown in these lines of code

# Step 1 - Data Preparation
df['text'] = df['text'].apply(clean)
df = df[df['text'].str.len() > 50]

if (runSVC):
    # Sample the data when running SVC to ensure reasonable run-times
    df = df.groupby('Component', as_index=False).apply(pd.DataFrame.sample,
                                                       random_state=42,
                                                       frac=.2)

# Step 2 - Train-Test Split
X_train, X_test, Y_train, Y_test = train_test_split(df['text'],
                                                    df['Component'],
                                                    test_size=0.2,
                                                    random_state=42,
                                                    stratify=df['Component'])
print('Size of Training Data ', X_train.shape[0])
print('Size of Test Data ', X_test.shape[0])

# Step 3 - Training the Machine Learning model
tfidf = TfidfVectorizer(stop_words="english")

if (runSVC):
    model = SVC(random_state=42, probability=True)
    grid_param = [{
        'tfidf__min_df': [5, 10],
        'tfidf__ngram_range': [(1, 3), (1, 6)],
        'model__C': [1, 100],
        'model__kernel': ['linear']
    }]
else:
    model = LinearSVC(random_state=42, tol=1e-5)
    grid_param = {
        'tfidf__min_df': [5, 10],
        'tfidf__ngram_range': [(1, 3), (1, 6)],
        'model__C': [1, 100],
        'model__loss': ['hinge']
    }

My question is: would the best_params found by the Grid Search using smaller dataset be actually best? Would a different best_params be found if we use the full dataset?