One of the files I'm including will be a replacement init. I'd like to have the replacement init include "displayserver -noauth" by default. If I do this, will it lock up a player that doesn't include displayserver? Or will it just print an error to the console and keep going?

It will just print an error and keep going. Or you could do the trick others use in the init and see if it exists before running it.

[ -e /usr/local/displayserver/displayserver ] && /usr/local/displayserver/displayserver -noauth