The statement is incorrect and it is obvious that it is correctincorrect. The first sentence is a misstatement of the central limit theorem. The second sentence is utter nonsense.
The sample mean is a number, not a distribution. What the CLT is about is the distribution of the means of a large number of samples from a population(s).
The answer to your question is "no" -- the larger the sample the more accurately it reflects the population (other things being equal).