I guess that rgojel means that it is the same as when a binomial with a large n and a small p is approximated with Poisson distribution. (The rule of thumb something like: n*p <7) and when the binomial or Poisson is approximated with a normal when n*p is large (rule of thumb: n*p>5 and n*(1-p) >5 or mu >5 in the Poisson case).

Please note that even if n is large and the response is approximate normal, the variance will still not be constant as it is influenced by p and mu.

The parameter estimates will still be approximately normal as usual in maximum likelihood estimation, provided that the sample is large enough.