That depends. If the problem has been solved before and the answer is known and it is in the corpus, then it can give you the correct answer without actually executing any code.
Is it not generally true? If the information (i.e. problem and its answer) exists in the model's training corpus, then LLMs can provide the correct answer without directly executing anything.
Ask it what the capital of France is, and it will tell you it is Paris. Same with "how do I reverse a string in Python", or whatever problem you have at hand that needs solving (sans searching capability, which makes things more complicated).
So does not the problem need to be unique if you want to be able to claim with certainty it indeed has been executed? I am not sure how you account for the searching capability, and I am not excluding the possibility of having access to execution tools, pretty sure they do.
