Can I hide the new messages notification in the Mail icon for only one of my email accounts?
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.