No, the "Turn off hard disk after" setting in the Power Plan does not apply to SSDs. It only applies to HDDs. For USB devices, there also exists a separate setting in the Power Plan. This setting can be found under USB Settings ➜ USB selective suspend.
If the internal Idle Timer of the HDD is enabled by factory default, then no, there is no way to prevent the HDD from falling asleep just by using Windows settings. That's why KeepAliveHD was invented. It might still be possible to disable the internal Idle Timer of the HDD each time after it gets re-enabled like I said, i.e. by using HDDScan each time after this happens, but not all HDDs that have the internal Idle Timer enabled by factory default let you disable it. A lot of them don't let you disable it, but KeepAliveHD should still work on all of them, i.e., regardless of the fact that a lot of them don't let you disable it. If it cannot be disabled, it means that neither HDDScan for Windows nor hdparm on Linux can be used to disable it, as it simply means that nothing can be used to disable it, but then, this doesn't stop KeepAliveHD from still letting you achieve your goal [of preventing your HDD from falling asleep].
