SATA is SATA. Apple has no special magic here. SATA is an international standard. SMART is another standard that has always worked by reading hardware data about the drive via the data connection (PATA or SATA). My Asus P8Z77 motherboard shows me a wealth of info about my drives this way:
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Since I'm an Independent Mac tech I don't typically see many Macs that are still within their Apple care timeframe. I have yet to do anything but software work on the late 2012. My previous comments were directed at the earlier iMac models.
If I owned your iMac I'd simply try a different drive. In OWC's video on RAM upgrades you can clearly see the Hitachi 1TB drive which doesn't have any Apple branding on it at all. My Guess is that you'd be safe with any Hitachi drive as a replacement, but I'd also bet that any drive would work with no special steps needed.
BTW I'm a beta tester for a major hard drive manufacturer and their replacement 2.5" 'Fusion' drive is in beta right now and is performing about midway between spinning HDD and SSD in terms of read/write tests. I think it may be a good solution for an iMac like yours (I have it in my i5 mini).