Hard drive failing?

I have a "late 2012" iMac with a 1 TB fusion drive running Yosemite. A couple of weeks ago SMART Reporter sent me an alert that my hard drive was soon going to fail. I ran Disk Utility and it verified the drive, saying it was OK. It was a very old version of SMART Reporter so I thought it might be a spurious report. I dowloaded the latest version and, until today, I got no alerts. But today SMART Reporter sent me another alert that the drive is failing.

I tried Disk Utility again. It verifies and says the disk is OK. But I noticed that it has no report of the SMART status shown. According to web sites I have looked at it's supposed to be there, but it's not. So should I assume my disk is dying, as SMART Reporter says, or assume it's OK, as Disk Utility says?

Additional questions: Does anyone know how long it would take Apple to repair the drive? I have an appointment at a local Apple store for Saturday afternoon. Also, since it's a fusion drive, will the machine still boot even if the spinning drive really does fail? If it will, can I assume that Mail, Safari, and other often-used applications are probably on the SSD and will still function?