Google Drive only works with the online Google Docs.
No, Google Drive (as an app) can be a resource to open documents that you open from another app. For example, if I open a document with Dropbox, I can then tap the button to open the document from another app that supports that format, and Google Drive is one of the options. I'll be prompted to upload the document to Google Drive, but the issue the OP is facing is that the originating app that isn't seeing Google Drive as an option.
I have the Google Drive app installed on my iPad, but it doesn't come up as an "open in" option for me in other apps. Does anyone know why this might be? Thanks!
That is entirely a limitation of whatever app you're starting with, or perhaps you don't have Google Drive installed? What are you starting to open the document with?