Distribute codec pack within application install

Is it allowed to include your codec pack within an application install if the application requires the codec pack to perform optimally?

Depends on what kind of app it is. You need to give some more details.

It is a proprietary presentation application. The pre-loaded videos play back smoother with the codec pack installed. Rather than have each user have to download and install the codec pack independently, we were looking to include it as part of our application install.

Use Basic or Standard version.
Make the installation of the codecs optional. This also makes it obvious to the end-user that it is included in your package.
Keep it up-to-date.