I want to be able to one-click email links from apps such as Twitter, Safari and Instapaper. Is this possible if I'm using Gmail and not Apple's Mail app?
Do I have to set Gmail as the default mail client? Is this possible?
This doesn't appear possible.
In order to utilize email functionalities from within apps, you will have to enable the Apple Mail app. I recommend turning off all notifications for Mail if you want to use the Gmail app as your primary iPhone mail client.
I do have a jailbroken iPhone 4s and unfortunately I cannot find any app to add this much desired functionality in any Cydia repository.
So at the moment I'd say it is not possible.