No, always there as both a character and an object.

I have nothing against the use of CGI where there's no other way to do something that needs to be done but IMO a model or a really good animatronic puppet or make-up will always look more "real" than CGI, especially in close-up. Even now, I watched Avatar on Blu-Ray the other day and it does look like an animated film for the most part, especially in 2D.

One other recent example is the Rise of the Planet of the Apes; while I thought the film itself was great, the monkeys looked incredibly fake. Now take a look at Tim Burton's PotA remake, they used animatronics and makeup and the monkeys look absolutely real.

Both technologies have their limitations, so it is usually a combination of both that yields the best results (like eg. in Jurassic Park).