Unfortunately, that's not possible right now, but we will consider adding such option in future updates. You're welcome to add a request to our Votebox: http://todoist.com/Vote_Android/
2 years passed. Still no way to show archived projects on Android. Any chance it will be added soon? I can archive from Android, but once its archived I can find it again only from the PC.
Unfortunately, there's no way to show archived projects yet. We're always looking into improving our Android and we may add this in the future.