I definitely wouldn't do it in production, but I've run Zimbra (postfix, jetty[java], apache, mysql and more) on a Linode 360 and it ran reasonably with no tuning. I did disable the anti-virus/anti-spam components--I'm not crazy
You didn't mention your traffic or where you've previously run this system, but since you're optimizing your platform to a high degree, I think you'll do well. I personally favor the Linode 1080 size; the 360s are for testing or things that can run more slowly.
If you don't want to jump to the next Linode size, you could always buy a bit more RAM under the Extras section of the Linode Manager (but upgrading is so much better--and cheaper overall).
Please let us know how it goes!