I'm not fully understanding the request. You want your phone to display/sync @me contacts, but only display the work@ contacts without syncing them? That's not a distinction that exists. The only way to display them is to sync them to your phone. That's the method by which they reach your phone.
Are you asking for it to not sync changes back from the phone to the work@ account? The only way to ensure that is, simply, not to make any changes to the work@ account contacts. Don't add anything to them, and don't edit them. The only things that sync back up to the cloud are things you change.
Syncing two different accounts (me@ and work@) will not merge the contacts. It will merge your view of those contacts, so that locally on your phone you see only one list of contacts aggregated from both sources, but if you go onto your computer, or work@ Gmail web interface, it will not contain all the contacts you synced to your phone from your me@ account. They're kept entirely walled off from each other. I have easily five or six Google accounts at any one time on my device, some Gmail, some Google Apps, and NONE of the contacts cross-pollinate. In fact I wish there was a way to make them do so, as it would be useful for me to have all of my contacts in a couple of those accounts for various purposes. But the moment I log into the web interface for one of my less common ones, I have zero access to any of the contacts in my primary one, and vice versa. So there should be zero problem here, just possibly the perception of one.
The only way to get the contacts from one into the other would be to manually export them from one account and import them into another. Or, presumably, use some sort of third-party app that might produce the same result.
Assuming my answers above don't clear up the issue, and there's still a problem, can you clarify a couple things for me?
- What specific phone do you have?
- Are you using the built-in Android function for adding these Google accounts, and not some third-party app to manage them?
- Do you have any sort of unusual backup apps you use on the phone for contacts?