Can I hide the new messages notification in the Mail icon for only one of my email accounts? Basically I would like to have two email accounts setup on my iPhone 4, one my personal account and one for work.

However for the work account, I'd like to not have it's unread message count included in the number of unread messages displayed as a part of the Mail app's icon (the number in the red circle).

Is this possible to do?
No - there's no control for that on iOS 4.3 or less. If you disable that account it will temporarily turn it off on counts but the content stays loaded on the device.

I will second the suggestion to set up a separate folder to store the majority of the unread messages and use server side filtering or a manual process to get rid of the distracting/offending messages. 

My phone and sanity are both better once I bit the bullet and set up a rule that says if it's unread over a week it goes into my triage later folder. I can still search for messages using spotlight, they are all where I can find them but my phone is faster and the badge is more meaningful without that pile of messages.

I'm not quite to inbox zero, but this was a good first step for me to getting there.