That depends on the controller and whether or not there is a write caching battery. This leads back to you saying it's probably a blanket statement. I think you're right there. The green drives may be just fine with a higher quality RAID controller with write caching but to be safe they just said no to RAID for the green drives.
Unlikely that the kind of controllers we are talking about, 2-4 drives, would have any kind of battery.
Even if they did, it wouldn't help. Every RAID controller is going to decide a drive is dead when it doesn't respond after some period of time. Once it decides it isn't going to automatically change it's mind. Even if it did keep retrying access after it has marked a drive dead it isn't going to automatically bring it back if it starts working again. The logic is if the drive didn't respond reasonably then there is something wrong with it. You don't want to start using a questionable drive again - and likely have it fail again. The longer you play games like that the higher the probability that other drive(s) in the RAID group will develop a problem which increases the risk of losing all integrity of your data. RAID is about reliability and one errs on the conservative side. Of course a manual intervention can tell the RAID controller to bring the drive back - with cheap no-knob RAID this is done by ejecting the drive and reinserting it.
My guess is that a "RED" drive is basically the same as a "GREEN" drive with some firmware tweaks (i.e. a few of the enterprise-class options).
I'd speculate that most/all the models are mostly the same physical device. Maybe the platters are graded/sorted. Possibly different speeds of the controller chip. Different cache RAM sizes. Different firmware (rpms, options, etc). The only reason to do all this complexity is price (to customer). Basically the physical device is mostly the same cost to manufacture no matter what model.