This depends entirely on the type of RAID (software or hardware) and the storage controller that is implementing RAID.
I'm the vast majority of implementations, there is no service interruption to the host system (that's the whole point of RAID). There is usually some kind of notification about the failure of a hard drive that an administrator must be made privy to. This is one of the most important parts of a RAID management system. I want to know how I can be made known of a failure. Something popping up to stderr or on the screen is of no use to anyone. You'll need email alerts, SMS gateways, SNMP traps and etc. so that you can monitor drive health from your NMS and / or get direct notification from the storage device that a failure has occurred.
In some cases, if there is a hot spare (ideally there is), the mirror immediately begins rebuilding. In that case, there is a performance degradation as the healthy drive is read from.