The correct answer is False.
A binomial random variable is a random variable that counts the number of successes in a sequence of independent experiments each of which yields success with probability $p$. A Gaussian random variable, also known as a normal random variable, is a random variable with a probability distribution that is bell-shaped.
The sum of iid Gaussian trials is a Gaussian random variable. However, the sum of iid binomial trials is not necessarily a Gaussian random variable. For example, if $X$ is a binomial random variable with parameters $n$ and $p$, then the sum of $n$ independent copies of $X$ is a binomial random variable with parameters $n^2$ and $p^2$. This is not a Gaussian random variable unless $p=0$ or $p=1$.
In conclusion, the binomial random variables are not obtained as the sum of iid Gaussian trials.