So there is HBA battery backup?
My entire FreeNAS server is on battery backup. If the power goes out, it does a clean shutdown after 5 minutes. So, if the "RAID controller", by virtue of software RAID, is the whole computer... and said computer is on battery backup... then fundamentally, yes: my RAID controller has a battery backup.
The end result is the same, just things are moved to different "rings" and the means to get there is a bit different, rocking older traditions from decades past. It requires thinking about things in a different manner and understanding the reasoning. While traditionally, computers were underpowered and hardware RAID was all the rage, times have changed. Main CPU processing capability has outgrown the fundamental needs of processing RAID negating the huge necessity and benefits of moving it off-CPU (once upon a time you needed to move floating-point math off-CPU too, but that eventually become no longer the case). Meanwhile, moving the raw management of RAID closer to the CPU allows far more-flexibility in the software app itself, which is something FreeNAS then depends on. Think of hardware RAID as being an automatic transmission, while FreeNAS is a professional driver who does better with a manual transmission and not so much automatic abstraction between him and what the gearbox is doing.