Does GridSearchCV store all the scores for all parameter combinations?

Yes it does, exactly as it is stated in the docs:

grid_scores_ : list of named tuples

Contains scores for all parameter combinations in param_grid. Each entry corresponds to one parameter setting. Each named tuple has the attributes:

• parameters, a dict of parameter settings
• mean_validation_score, the mean score over the cross-validation folds
• cv_validation_scores, the list of scores for each fold

allscores=model.cv_results_['mean_test_score']
print(allscores)