How to check if a signal is mainly composed of a few impulse peaks?
You can use kurtosis as a measure of how 'peaky' your signal is. Or the flatness measure, which is the ratio of the geometric mean of the signal to its arithmetic mean. Any signal which is not relatively flat will have a flatness value near 0.
$$\text{Flatness} = \frac{\sqrt[N]{\prod_{n=0}^{N-1} x(n)}}{\frac{1}{N} \sum_{n=0}^{N-1} x(n)}$$