It really depends on the circumstances. It's not uncommon to keep a little on the underexposed side with white birds when they are against middle tone or darker backgrounds. However, a white bird on sand or against snow will underexpose for sure. A white bird that's filling most of the frame is also prone to underexposure, so you have to be careful.
Still, with most modern Nikons (i.e. not the D5/6), there is no real penalty for underexposing a little. It'll add a little noise in post, but nothing more than had you shot at an equivalent ISO in the field. (i.e. if you used ISO 400 in the field but really needed ISO 800, when you brighten the exposure in post by a stop, it will look like it was shot at ISO 800).
Of course, this assumes you're shooting RAW.
By the way, there are times I REALLY underexpose my subject if I'm trying to protect highlights. The trick is to keep the ISO as low as possible so when you pull the exposure back up, things don't get too noisy.