Contact form does not depend on smtp except to forward the message, it keeps messages in the database and messages can be viewed by clicking the view messages link next to the title of the contact form. So there is no reason to inform a user if some error happens on contact form.
Also email is not transactional and has no guarantee of delivery, a message can be relayed with no error happening at the time of relay but it still may fail and bounce back later. If an error happens while trying to relay the message then the error is logged so site admins should review their logs frequently. There is no way to ever know for sure after relaying an email message that it succeeded or not unless you are the recipient.