If I have a complete application, and I want to make it very easy to install, is it appropriate to publish it as a package on packagist.org? Or is packagist intended only for the dependencies you use for putting together other applications?
The objective is to make the most of Composer to make installation easy.
Quote from https://packagist.org/about :
Packagist is the default Composer package repository. It lets you find packages and lets Composer know where to get the code from. You can use Composer to manage your project or libraries' dependencies...
So it should be perfectly fine to use it like you want.