What I was suggesting is, you create a throwaway gmail account. Then you set that account up so that it pulls all of your emails from the google apps account (POP only I'm afraid
) and set it up so your gmail account can send mail via your google apps acount (and does so by default).
For all intents and purposes you have now got your non-gmail email address working with the gmail app
I do this for my university email address, for example.
The only weak link is the fact the gmail account pulls emails down via POP and you cannot set how often it does this. Sometimes you can be waiting a good few minutes for emails to appear. I imagine if you set it up so that the google apps account forwarded to the gmail account in stead it would be better, but I haven't tried this.