Determining whether or not a system is BIBO stable
In your case

$$\int_{-\infty}^{\infty}|h(t)|dt=\int_{-\infty}^{\infty}h(t)dt=
\int_{-\infty}^{\infty}\sum_{n=-\infty}^{\infty}\delta(t-2n)dt=
\sum_{n=-\infty}^{\infty}\int_{-\infty}^{\infty}\delta(t-2n)dt$$

And since

$$\int_{-\infty}^{\infty}\delta(t-2n)dt=1$$

(as correctly pointed out by Dilip Sarwate in his comment to Phonon's answer), the above sum is

$$\sum_{n=-\infty}^{\infty}1=1+1+1+\ldots=\infty$$

I believe that this is basically the argument you gave in your question.