I used to work for a company that fed all replies to a custom CRM system which filtered out of office and bounces (unsubscribing on hard bounces automatically) and it worked great!

Those are enquiries from your (potential) customers. That's what you have support & sales people for!

It's strange that there are companies paying fortune to funnel people from AdWords to their sales enquiry form, but refuse to look at enquiries via e-mail.