I believe so. This is something I had to prove sometime back. It's a cool proof.

Let . Therefore,

Start with the binomial

Now, if we divide one of the x factors, n, in into each factor of the product , and then write

we get:

Now, let while x and lambda stay fixed.

we get:

Now, we get the famous 'e' limit:

Therefore, hence, and heretofore, we get:

and the limiting distribution becomes the Poisson distribution.