Hi,
generally, additional biding (another port) with some other certificate must not cause any problems with agent connectivity. Agents will just not know about it. I know that setting another certificate for same port will break connectivity. This is kind of unsupported configuration that can't be set from IIS UI for example.
If you want to replace existing web certificate with other one, use Certificate Management page in NS console. Settings - Notification Server - Certificate Management. Select "NS web site certificate" and initiate replacement operation. It will take care of updating connection profiles etc. As soon as agents will get info about new NS web certificate, you will be able to finalize replacement operation from same UI - old certificate will be removed from profiles and new certificate will be set for binding.
Thanks,
Ed.